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We discuss how string theory, and in particular the "fuzzball" paradigm, has already made and can make meaningful contributions to the phenomenology of strong gravity observations. We outline pertinent research directions for the near-future within this program, and emphasize the unique viewpoints that string theory and fuzzballs bring to phenomenology., Comment: 9 pages

We discuss how string theory, and in particular the "fuzzball" paradigm, has already made and can make meaningful contributions to the phenomenology of strong gravity observations. We outline pertinent research directions for the near-future within this program, and emphasize the unique viewpoints that string theory and fuzzballs bring to phenomenology., Comment: 9 pages

We discuss how string theory, and in particular the "fuzzball" paradigm, has already made and can make meaningful contributions to the phenomenology of strong gravity observations. We outline pertinent research directions for the near-future within this program, and emphasize the unique viewpoints that string theory and fuzzballs bring to phenomenology., Comment: 9 pages

We study the physical properties of four-dimensional, string-theoretical, horizonless "fuzzball" geometries by imaging their shadows. Their microstructure traps light rays straying near the would-be horizon on long-lived, highly redshifted chaotic orbits. In fuzzballs sufficiently near the scaling limit this creates a shadow much like that of a black hole, while avoiding the paradoxes associated with an event horizon. Observations of the shadow size and residual glow can potentially discriminate between fuzzballs away from the scaling limit and alternative models of black compact objects., Comment: 6 pages, 3 figures

Contains fulltext : 239191.pdf (Publisher’s version ) (Open Access)

Contains fulltext : 239191.pdf (Publisher’s version ) (Open Access)

Contains fulltext : 239191.pdf (Publisher’s version ) (Open Access)

We study the physical properties of four-dimensional, string-theoretical, horizonless "fuzzball" geometries by imaging their shadows. Their microstructure traps light rays straying near the would-be horizon on long-lived, highly redshifted chaotic orbits. In fuzzballs sufficiently near the scaling limit this creates a shadow much like that of a black hole, while avoiding the paradoxes associated with an event horizon. Observations of the shadow size and residual glow can potentially discriminate between fuzzballs away from the scaling limit and alternative models of black compact objects., Comment: 6 pages, 3 figures

We study the physical properties of four-dimensional, string-theoretical, horizonless "fuzzball" geometries by imaging their shadows. Their microstructure traps light rays straying near the would-be horizon on long-lived, highly redshifted chaotic orbits. In fuzzballs sufficiently near the scaling limit this creates a shadow much like that of a black hole, while avoiding the paradoxes associated with an event horizon. Observations of the shadow size and residual glow can potentially discriminate between fuzzballs away from the scaling limit and alternative models of black compact objects., Comment: 6 pages, 3 figures

Gravitational wave observations of the near-horizon region of black holes lend insight into the quantum nature of gravity. In particular, gravitational wave echoes have been identified as a potential signature of quantum gravity-inspired structure near the horizon. In this paper, we connect such observables to the language of black hole microstates in string theory and holography. To that end, we propose a toy model describing the AdS$_3$ near-horizon region of five-dimensional black holes, inspired by earlier work of Solodukhin. This model captures key features of recently constructed microstate geometries, and allows us to make three observations. First, we relate the language of AdS/CFT, in particular the holographic retarded two-point correlator, to effective parameters modeling the structure that are used in flat space gravitational wave literature. Second, we find that for a typical microstate, the `cap' of the microstructure is exponentially close to the horizon, making it an effective sub-Planckian correction to the black hole geometry, although the microstate geometry itself is classical. Third, using a microcanonical ensemble average over geometries, we find support for the claim that the gravitational wave echo amplitude in a typical quantum microstate of the black hole is exponentially suppressed by the black hole entropy., Comment: 47 pages

The event horizon of a black hole in general relativity absorbs all infalling radiation. Any observation of the contrary would immediately challenge the expectation that astrophysical black holes are described by the vacuum Kerr geometry. If a putative black hole does reflect part of the ingoing radiation, its quasinormal mode structure is drastically altered. Low frequency modes can be introduced that are resonantly excited during the inspiral of a binary system. We study the resulting phase shift of the gravitational wave signal. Building on neutron star results, we obtain a model-independent expression for the phase shift that depends only on quasinormal modes and Love numbers of the compact object. We find that the phase shift might be detectable with Einstein Telescope for asymmetric binaries in high signal-to-noise events ($\sim 10^3$), but by far cannot explore the Planck scale., Comment: 23 pages, 3 figures. Fixed error, modified detection prospects

We develop a systematic ray-tracing method which can be used to explore a wide class of higher-dimensional multi-center black objects through the shape of their shadows. As a proof of principle, we test our method by imaging black holes and black rings in five dimensions. Two-dimensional slices of the three-dimensional shadows of those five-dimensional black objects not only show new phenomena, such as the first image of a toroidal horizon, but also offer a new viewpoint on black holes and binary systems in four dimensions., Comment: 30 pages, 8 figures. v2: reference updated

The grand challenges of contemporary fundamental physics dark matter, dark energy, vacuum energy, inflation and early universe cosmology, singularities and the hierarchy problem all involve gravity as a key component. And of all gravitational phenomena, black holes stand out in their elegant simplicity, while harbouring some of the most remarkable predictions of General Relativity: event horizons, singularities and ergoregions. The hitherto invisible landscape of the gravitational Universe is being unveiled before our eyes: the historical direct detection of gravitational waves by the LIGO-Virgo collaboration marks the dawn of a new era of scientific exploration. Gravitational-wave astronomy will allow us to test models of black hole formation, growth and evolution, as well as models of gravitational-wave generation and propagation. It will provide evidence for event horizons and ergoregions, test the theory of General Relativity itself, and may reveal the existence of new fundamental fields. The synthesis of these results has the potential to radically reshape our understanding of the cosmos and of the laws of Nature. The purpose of this work is to present a concise, yet comprehensive overview of the state of the art in the relevant fields of research, summarize important open problems, and lay out a roadmap for future progress. This write-up is an initiative taken within the framework of the European Action on 'Black holes, Gravitational waves and Fundamental Physics'.

We develop a systematic ray-tracing method which can be used to explore a wide class of higher-dimensional multi-center black objects through the shape of their shadows. As a proof of principle, we test our method by imaging black holes and black rings in five dimensions. Two-dimensional slices of the three-dimensional shadows of those five-dimensional black objects not only show new phenomena, such as the first image of a toroidal horizon, but also offer a new viewpoint on black holes and binary systems in four dimensions., Comment: 30 pages, 8 figures. v2: reference updated

The grand challenges of contemporary fundamental physics-dark matter, dark energy, vacuum energy, inflation and early universe cosmology, singularities and the hierarchy problem-all involve gravity as a key component. And of all gravitational phenomena, black holes stand out in their elegant simplicity, while harbouring some of the most remarkable predictions of General Relativity: event horizons, singularities and ergoregions. The hitherto invisible landscape of the gravitational Universe is being unveiled before our eyes: the historical direct detection of gravitational waves by the LIGO-Virgo collaboration marks the dawn of a new era of scientific exploration. Gravitational-wave astronomy will allow us to test models of black hole formation, growth and evolution, as well as models of gravitational-wave generation and propagation. It will provide evidence for event horizons and ergoregions, test the theory of General Relativity itself, and may reveal the existence of new fundamental fields. The synthesis of these results has the potential to radically reshape our understanding of the cosmos and of the laws of Nature. The purpose of this work is to present a concise, yet comprehensive overview of the state of the art in the relevant fields of research, summarize important open problems, and lay out a roadmap for future progress. This write-up is an initiative taken within the framework of the European Action on 'Black holes, Gravitational waves and Fundamental Physics'.

We study the supersymmetry breaking induced by probe anti-D3-branes at the tip of the Klebanov-Strassler throat geometry. Antibranes inside this geometry polarize and can be described by an NS5-brane wrapping an $S^2$. When the number of antibranes is small compared to the background flux a metastable state exists that breaks supersymmetry. We present a manifestly supersymmetric effective model that realizes the polarized metastable state as a solution, spontaneously breaking the supersymmetry. The supersymmetric model relies crucially on the inclusion of Kaluza-Klein (matrix) degrees of freedom on the $S^2$ and two supersymmetric irrelevant deformations of ${\cal N}=4$ super-Yang-Mills (SYM), describing a large number of supersymmetric D3-branes in the IR. We explicitly identify the massless Goldstino and compute the spectrum of massive fluctuations around the metastable supersymmetry-breaking minimum, finding a Kaluza-Klein tower with masses warped down from the string scale. Below the Kaluza-Klein scale the massive tower can be integrated out and supersymmetry is realized nonlinearly. We comment on the effect of the Kaluza-Klein modes on the effective description of de Sitter vacua in string theory and inflationary model building., Comment: v1: 9 pages, v2: added references, changed title slightly and fixed typos

The grand challenges of contemporary fundamental physics---dark matter, dark energy, vacuum energy, inflation and early universe cosmology, singularities and the hierarchy problem---all involve gravity as a key component. And of all gravitational phenomena, black holes stand out in their elegant simplicity, while harbouring some of the most remarkable predictions of General Relativity: event horizons, singularities and ergoregions. The hitherto invisible landscape of the gravitational Universe is being unveiled before our eyes: the historical direct detection of gravitational waves by the LIGO-Virgo collaboration marks the dawn of a new era of scientific exploration. Gravitational-wave astronomy will allow us to test models of black hole formation, growth and evolution, as well as models of gravitational-wave generation and propagation. It will provide evidence for event horizons and ergoregions, test the theory of General Relativity itself, and may reveal the existence of new fundamental fields. The synthesis of these results has the potential to radically reshape our understanding of the cosmos and of the laws of Nature. The purpose of this work is to present a concise, yet comprehensive overview of the state of the art in the relevant fields of research, summarize important open problems, and lay out a roadmap for future progress., Comment: White Paper for the COST action "Gravitational Waves, Black Holes, and Fundamental Physics", 272 pages, 12 figures; v4: updated references and author list. Overall improvements and corrections. To appear in Classical and Quantum Gravity

We study the supersymmetry breaking induced by probe anti-D3-branes at the tip of the Klebanov-Strassler throat geometry. Antibranes inside this geometry polarize and can be described by an NS5-brane wrapping an $S^2$. When the number of antibranes is small compared to the background flux a metastable state exists that breaks supersymmetry. We present a manifestly supersymmetric effective model that realizes the polarized metastable state as a solution, spontaneously breaking the supersymmetry. The supersymmetric model relies crucially on the inclusion of Kaluza-Klein (matrix) degrees of freedom on the $S^2$ and two supersymmetric irrelevant deformations of ${\cal N}=4$ super-Yang-Mills (SYM), describing a large number of supersymmetric D3-branes in the IR. We explicitly identify the massless Goldstino and compute the spectrum of massive fluctuations around the metastable supersymmetry-breaking minimum, finding a Kaluza-Klein tower with masses warped down from the string scale. Below the Kaluza-Klein scale the massive tower can be integrated out and supersymmetry is realized nonlinearly. We comment on the effect of the Kaluza-Klein modes on the effective description of de Sitter vacua in string theory and inflationary model building., Comment: v1: 9 pages, v2: added references, changed title slightly and fixed typos

The grand challenges of contemporary fundamental physics---dark matter, dark energy, vacuum energy, inflation and early universe cosmology, singularities and the hierarchy problem---all involve gravity as a key component. And of all gravitational phenomena, black holes stand out in their elegant simplicity, while harbouring some of the most remarkable predictions of General Relativity: event horizons, singularities and ergoregions. The hitherto invisible landscape of the gravitational Universe is being unveiled before our eyes: the historical direct detection of gravitational waves by the LIGO-Virgo collaboration marks the dawn of a new era of scientific exploration. Gravitational-wave astronomy will allow us to test models of black hole formation, growth and evolution, as well as models of gravitational-wave generation and propagation. It will provide evidence for event horizons and ergoregions, test the theory of General Relativity itself, and may reveal the existence of new fundamental fields. The synthesis of these results has the potential to radically reshape our understanding of the cosmos and of the laws of Nature. The purpose of this work is to present a concise, yet comprehensive overview of the state of the art in the relevant fields of research, summarize important open problems, and lay out a roadmap for future progress., Comment: White Paper for the COST action "Gravitational Waves, Black Holes, and Fundamental Physics", 272 pages, 12 figures; v4: updated references and author list. Overall improvements and corrections. To appear in Classical and Quantum Gravity

Structure at the horizon scale of black holes would give rise to echoes of the gravitational wave signal associated with the post-merger ringdown phase in binary coalescences. We study the waveform of echoes in static and stationary, traversable wormholes in which perturbations are governed by a symmetric effective potential. We argue that echoes are dominated by the wormhole quasinormal frequency nearest to the fundamental black hole frequency that controls the primary signal. We put forward an accurate method to construct the echoes waveform(s) from the primary signal and the quasinormal frequencies of the wormhole, which we characterize. We illustrate this in the static Damour-Solodukhin wormhole and in a new, rotating generalization that approximates a Kerr black hole outside the throat. Rotation gives rise to a potential with an intermediate plateau region that breaks the degeneracy of the quasinormal frequencies. Rotation also leads to late-time instabilities which, however, fade away for small angular momentum., Comment: 17 pages, 10 figures, 1 table; v3: minor modifications to match published version

We construct a new class of metastable de Sitter vacua of flux compactifications of type IIB string theory. These solutions provide a natural extension of the `Large Volume Scenario' anti-de Sitter vacua, and can analogously be realised at parametrically large volume and weak string coupling, using standard ${\cal N}=1$ supergravity. For these new vacua, a positive vacuum energy is achieved from the inclusion of a small amount of flux-induced supersymmetry breaking in the complex structure and axio-dilaton sector, and no additional `uplift' contribution (e.g.~from anti-branes) is required. We show that the approximate no-scale structure of the effective theory strongly influences the spectrum of the stabilised moduli: one complex structure modulus remains significantly lighter than the supersymmetry breaking scale, and metastability requires only modest amounts of tuning. After discussing these general results, we provide a recipe for constructing de Sitter vacua on a given compactification manifold, and give an explicit example of a de Sitter vacuum for the compactification on the Calabi-Yau orientifold realised in $\mathbb{CP}^4_{11169}$. Finally, we note that these solutions have intriguing implications for phenomenology, predicting no superpartners in the spectrum below $\sim$50 TeV, and no WIMP dark matter., Comment: 34 pages

We study the effect of brane polarization on the supersymmetry transformations of probe anti-D3-branes at the tip of a Klebanov-Strassler throat geometry. As is well known, the probe branes can polarize into NS5-branes and decay to a supersymmetric state by brane-flux annihilation. The effective potential has a metastable minimum as long as the number of anti-D3-branes is small compared to the number of flux quanta. We study the reduced four-dimensional effective NS5-brane theory and show that in the metastable minimum supersymmetry is non-linearly realized to leading order, as expected for spontaneously broken supersymmetry. However, a strict decoupling limit of the higher order corrections in terms of a standard nilpotent superfield does not seem to exist. We comment on the possible implications of these results for more general low-energy effective descriptions of inflation or de Sitter vacua., Comment: 22 pages, 1 figure. v2: fixed typos, matches published version

Structure at the horizon scale of black holes would give rise to echoes of the gravitational wave signal associated with the post-merger ringdown phase in binary coalescences. We study the waveform of echoes in static and stationary, traversable wormholes in which perturbations are governed by a symmetric effective potential. We argue that echoes are dominated by the wormhole quasinormal frequency nearest to the fundamental black hole frequency that controls the primary signal. We put forward an accurate method to construct the echoes waveform(s) from the primary signal and the quasinormal frequencies of the wormhole, which we characterize. We illustrate this in the static Damour-Solodukhin wormhole and in a new, rotating generalization that approximates a Kerr black hole outside the throat. Rotation gives rise to a potential with an intermediate plateau region that breaks the degeneracy of the quasinormal frequencies. Rotation also leads to late-time instabilities which, however, fade away for small angular momentum., Comment: 17 pages, 10 figures, 1 table; v3: minor modifications to match published version

We construct a new class of metastable de Sitter vacua of flux compactifications of type IIB string theory. These solutions provide a natural extension of the `Large Volume Scenario' anti-de Sitter vacua, and can analogously be realised at parametrically large volume and weak string coupling, using standard ${\cal N}=1$ supergravity. For these new vacua, a positive vacuum energy is achieved from the inclusion of a small amount of flux-induced supersymmetry breaking in the complex structure and axio-dilaton sector, and no additional `uplift' contribution (e.g.~from anti-branes) is required. We show that the approximate no-scale structure of the effective theory strongly influences the spectrum of the stabilised moduli: one complex structure modulus remains significantly lighter than the supersymmetry breaking scale, and metastability requires only modest amounts of tuning. After discussing these general results, we provide a recipe for constructing de Sitter vacua on a given compactification manifold, and give an explicit example of a de Sitter vacuum for the compactification on the Calabi-Yau orientifold realised in $\mathbb{CP}^4_{11169}$. Finally, we note that these solutions have intriguing implications for phenomenology, predicting no superpartners in the spectrum below $\sim$50 TeV, and no WIMP dark matter., Comment: 34 pages

We study the effect of brane polarization on the supersymmetry transformations of probe anti-D3-branes at the tip of a Klebanov-Strassler throat geometry. As is well known, the probe branes can polarize into NS5-branes and decay to a supersymmetric state by brane-flux annihilation. The effective potential has a metastable minimum as long as the number of anti-D3-branes is small compared to the number of flux quanta. We study the reduced four-dimensional effective NS5-brane theory and show that in the metastable minimum supersymmetry is non-linearly realized to leading order, as expected for spontaneously broken supersymmetry. However, a strict decoupling limit of the higher order corrections in terms of a standard nilpotent superfield does not seem to exist. We comment on the possible implications of these results for more general low-energy effective descriptions of inflation or de Sitter vacua., Comment: 22 pages, 1 figure. v2: fixed typos, matches published version

Structure at the horizon scale of black holes would give rise to echoes of the gravitational wave signal associated with the post-merger ringdown phase in binary coalescences. We study the waveform of echoes in static and stationary, traversable wormholes in which perturbations are governed by a symmetric effective potential. We argue that echoes are dominated by the wormhole quasinormal frequency nearest to the fundamental black hole frequency that controls the primary signal. We put forward an accurate method to construct the echoes waveform(s) from the primary signal and the quasinormal frequencies of the wormhole, which we characterize. We illustrate this in the static Damour-Solodukhin wormhole and in a new, rotating generalization that approximates a Kerr black hole outside the throat. Rotation gives rise to a potential with an intermediate plateau region that breaks the degeneracy of the quasinormal frequencies. Rotation also leads to late-time instabilities which, however, fade away for small angular momentum., Comment: 17 pages, 10 figures, 1 table; v3: minor modifications to match published version

Structure at the horizon scale of black holes would give rise to echoes of the gravitational wave signal associated with the post-merger ringdown phase in binary coalescences. We study the waveform of echoes in static and stationary, traversable wormholes in which perturbations are governed by a symmetric effective potential. We argue that echoes are dominated by the wormhole quasinormal frequency nearest to the fundamental black hole frequency that controls the primary signal. We put forward an accurate method to construct the echoes waveform(s) from the primary signal and the quasinormal frequencies of the wormhole, which we characterize. We illustrate this in the static Damour-Solodukhin wormhole and in a new, rotating generalization that approximates a Kerr black hole outside the throat. Rotation gives rise to a potential with an intermediate plateau region that breaks the degeneracy of the quasinormal frequencies. Rotation also leads to late-time instabilities which, however, fade away for small angular momentum., Comment: 17 pages, 10 figures, 1 table; v3: minor modifications to match published version

The KKLT construction of dS vacua relies on an uplift term that arises from an anti-D3-brane. It was argued by Kachru, Pearson and Verlinde that this anti-D3-brane is an excited state in a supersymmetric theory since it can decay to a supersymmetric ground state. Hence the anti-D3-brane breaks supersymmetry spontaneously and one should be able to package all the world-volume fields on the anti-D3-brane into a four dimensional $\cal{N}=1$ supersymmetric action. Here we extend previous results and identify the constrained superfields that correspond to all the degrees of freedom on the anti-D3-brane. In particular, we show explicitly that the four 4D worldvolume spinors give rise to constrained chiral multiplets $S$ and $Y^i$, $i=1,2,3$ that satisfy $S^2=SY^i=0$. We also conjecture (and provide evidence in a forthcoming publication) that the vector field $A_\mu$ and the three scalars $\phi^i$ give rise to a field strength multiplet $W_\alpha$ and three chiral multiplets $H^i$ that satisfy the constraints $S W_\alpha= \bar{D}_{\dot \alpha} (S \bar H^i)=0$. This is the first time that such constrained multiplets appear in string theory constructions., Comment: 20 pages, v2: references added

We study the non-linearly realized spontaneously broken supersymmetry of the (anti-)D3-brane action in type IIB string theory. The worldvolume fields are one vector $A_\mu$, three complex scalars $\phi^i$ and four 4d fermions $\lambda^0$, $\lambda^i$. These transform, in addition to the more familiar N=4 linear supersymmetry, also under 16 spontaneously broken, non-linearly realized supersymmetries. We argue that the worldvolume fields can be packaged into the following constrained 4d non-linear N=1 multiplets: four chiral multiplets $S$, $Y^i$ that satisfy $S^2=SY^i=0$ and contain the worldvolume fermions $\lambda^0$ and $\lambda^i$; and four chiral multiplets $W_\alpha$, $H^i$ that satisfy $S W_\alpha=0$ and $S \bar D_{\dot \alpha} \bar H^{\bar \imath}=0$ and contain the vector $A_\mu$ and the scalars $\phi^i$. We also discuss how placing an anti-D3-brane on top of intersecting O7-planes can lead to an orthogonal multiplet $\Phi$ that satisfies $S(\Phi-\bar \Phi)=0$, which is particularly interesting for inflationary cosmology., Comment: 28 pages, v2: published version, 1 reference added

The KKLT construction of dS vacua relies on an uplift term that arises from an anti-D3-brane. It was argued by Kachru, Pearson and Verlinde that this anti-D3-brane is an excited state in a supersymmetric theory since it can decay to a supersymmetric ground state. Hence the anti-D3-brane breaks supersymmetry spontaneously and one should be able to package all the world-volume fields on the anti-D3-brane into a four dimensional $\cal{N}=1$ supersymmetric action. Here we extend previous results and identify the constrained superfields that correspond to all the degrees of freedom on the anti-D3-brane. In particular, we show explicitly that the four 4D worldvolume spinors give rise to constrained chiral multiplets $S$ and $Y^i$, $i=1,2,3$ that satisfy $S^2=SY^i=0$. We also conjecture (and provide evidence in a forthcoming publication) that the vector field $A_\mu$ and the three scalars $\phi^i$ give rise to a field strength multiplet $W_\alpha$ and three chiral multiplets $H^i$ that satisfy the constraints $S W_\alpha= \bar{D}_{\dot \alpha} (S \bar H^i)=0$. This is the first time that such constrained multiplets appear in string theory constructions., Comment: 20 pages, v2: references added

We study the non-linearly realized spontaneously broken supersymmetry of the (anti-)D3-brane action in type IIB string theory. The worldvolume fields are one vector $A_\mu$, three complex scalars $\phi^i$ and four 4d fermions $\lambda^0$, $\lambda^i$. These transform, in addition to the more familiar N=4 linear supersymmetry, also under 16 spontaneously broken, non-linearly realized supersymmetries. We argue that the worldvolume fields can be packaged into the following constrained 4d non-linear N=1 multiplets: four chiral multiplets $S$, $Y^i$ that satisfy $S^2=SY^i=0$ and contain the worldvolume fermions $\lambda^0$ and $\lambda^i$; and four chiral multiplets $W_\alpha$, $H^i$ that satisfy $S W_\alpha=0$ and $S \bar D_{\dot \alpha} \bar H^{\bar \imath}=0$ and contain the vector $A_\mu$ and the scalars $\phi^i$. We also discuss how placing an anti-D3-brane on top of intersecting O7-planes can lead to an orthogonal multiplet $\Phi$ that satisfies $S(\Phi-\bar \Phi)=0$, which is particularly interesting for inflationary cosmology., Comment: 28 pages, v2: published version, 1 reference added

Collapsing shells form horizons, and when the curvature is small classical general relativity is believed to describe this process arbitrarily well. On the other hand, quantum information theory based (fuzzball/firewall) arguments suggest the existence of some structure at the black hole horizon. This structure can only form if classical general relativity stops being the correct description of the collapsing shell before it reaches the horizon size. We present strong evidence that classical general relativity can indeed break down prematurely, by explicitly computing the quantum tunneling amplitude of a collapsing shell of branes into smooth horizonless microstate geometries. We show that the amplitude for tunneling into microstate geometries with a large number of topologically non-trivial cycles is parametrically larger than exp(-S), which indicates that the shell can tunnel into a horizonless configuration long before the horizon has any chance to form. We also use this technology to investigate the tunneling of M2 branes into LLM bubbling geometries., Comment: 26 pages + appendix

Supersymmetry-breaking is a key ingredient for string theory models to be phenomenologically viable. We review the strong analogy in the physics and the methods used for describing non-supersymmetric flux vacua and non-supersymmetric black holes in string theory. We also show how the polarized state could be the key to describing a well-behaved back-reaction of anti-branes in flux backgrounds, shedding a new light on a recent debate in the literature., Comment: 5 pages, slightly extended contribution to the proceedings of the 21st European String Workshop: "The String Theory Universe" in Leuven, 7-11 Sept 2015

We revisit necessary conditions for gluing local (anti-)D3 throats into flux throats with opposite charge. These consistency conditions typically reveal singularities in the three-form fluxes whose meaning is being debated. In this note we prove, under well-motivated assumptions, that unphysical singularities can potentially be avoided when the anti-branes polarise into spherical NS5 branes with a specific radius. If a consistent solution can then indeed be found, our analysis seems to suggests a rather large correction to the radius of the polarization sphere compared to the probe result. We furthermore comment on the gluing conditions at finite temperature and point out that one specific assumption of a recent no-go theorem can be broken if anti-branes are indeed to polarise into spherical NS5 branes at zero temperature., Comment: 17 pages, 2 figures, v2: error corrected and text extended

We investigate the structure of smooth and horizonless microstate geometries in six dimensions, in the spirit of the five-dimensional analysis of Gibbons and Warner [arXiv:1305.0957]. In six dimensions, which is the natural setting for horizonless geometries with the charges of the D1-D5-P black hole, the natural black objects are strings and there are no Chern-Simons terms for the tensor gauge fields. However, we still find that the same reasoning applies: in absence of horizons, there can be no smooth stationary solutions without non-trivial topology. We use topological arguments to describe the Smarr formula in various examples: the uplift of the five-dimensional minimal supergravity microstates to six dimensions, the two-charge D1-D5 microstates, and the non-extremal JMaRT solution. We also discuss D1-D5-P superstrata and confirm that the Smarr formula gives the same result as for the D1-D5 supertubes which are topologically equivalent., Comment: 29 pages, v2: references added, published version

Collapsing shells form horizons, and when the curvature is small classical general relativity is believed to describe this process arbitrarily well. On the other hand, quantum information theory based (fuzzball/firewall) arguments suggest the existence of some structure at the black hole horizon. This structure can only form if classical general relativity stops being the correct description of the collapsing shell before it reaches the horizon size. We present strong evidence that classical general relativity can indeed break down prematurely, by explicitly computing the quantum tunneling amplitude of a collapsing shell of branes into smooth horizonless microstate geometries. We show that the amplitude for tunneling into microstate geometries with a large number of topologically non-trivial cycles is parametrically larger than exp(-S), which indicates that the shell can tunnel into a horizonless configuration long before the horizon has any chance to form. We also use this technology to investigate the tunneling of M2 branes into LLM bubbling geometries., Comment: 26 pages + appendix

Supersymmetry-breaking is a key ingredient for string theory models to be phenomenologically viable. We review the strong analogy in the physics and the methods used for describing non-supersymmetric flux vacua and non-supersymmetric black holes in string theory. We also show how the polarized state could be the key to describing a well-behaved back-reaction of anti-branes in flux backgrounds, shedding a new light on a recent debate in the literature., Comment: 5 pages, slightly extended contribution to the proceedings of the 21st European String Workshop: "The String Theory Universe" in Leuven, 7-11 Sept 2015

We revisit necessary conditions for gluing local (anti-)D3 throats into flux throats with opposite charge. These consistency conditions typically reveal singularities in the three-form fluxes whose meaning is being debated. In this note we prove, under well-motivated assumptions, that unphysical singularities can potentially be avoided when the anti-branes polarise into spherical NS5 branes with a specific radius. If a consistent solution can then indeed be found, our analysis seems to suggests a rather large correction to the radius of the polarization sphere compared to the probe result. We furthermore comment on the gluing conditions at finite temperature and point out that one specific assumption of a recent no-go theorem can be broken if anti-branes are indeed to polarise into spherical NS5 branes at zero temperature., Comment: 17 pages, 2 figures, v2: error corrected and text extended

We investigate the structure of smooth and horizonless microstate geometries in six dimensions, in the spirit of the five-dimensional analysis of Gibbons and Warner [arXiv:1305.0957]. In six dimensions, which is the natural setting for horizonless geometries with the charges of the D1-D5-P black hole, the natural black objects are strings and there are no Chern-Simons terms for the tensor gauge fields. However, we still find that the same reasoning applies: in absence of horizons, there can be no smooth stationary solutions without non-trivial topology. We use topological arguments to describe the Smarr formula in various examples: the uplift of the five-dimensional minimal supergravity microstates to six dimensions, the two-charge D1-D5 microstates, and the non-extremal JMaRT solution. We also discuss D1-D5-P superstrata and confirm that the Smarr formula gives the same result as for the D1-D5 supertubes which are topologically equivalent., Comment: 29 pages, v2: references added, published version

We study ${\cal N}=1$ supergravity with $N>1$ chiral superfields in which one of the fields has a K\"ahler potential of exact no-scale type. Such systems admit de Sitter (dS) solutions in which supersymmetry is predominantly broken by the no-scale field, with only a small contribution to the breaking coming from the other fields. Metastable dS vacua of this type were recently shown to be achievable by the finetuning of an $N\times N$ sub-matrix of the Hessian matrix at the critical point. We show that perturbatively small deformations of the no-scale Minkowski vacuum into dS are only possible when the spectrum of the no-scale vacuum, besides the no-scale field, contain an additional massless mode. The no-scale structure allows for a decoupling of $N-2$ fields, and metastability can be achieved by the tuning of ${\cal O}(N^0)$ parameters. We illustrate this scenario in several examples, and derive a geometric condition for its realisation in type IIB string theory. Supergravities in which the complex structure moduli space is a symmetric space, such as the string theory inspired STU-models, are non-generic and realise a modified version of the scenario. For the STU-model with a single non-perturbative correction we present an explicit analytic family of dS solutions that includes examples with quantised fluxes satisfying the O3-plane tadpole condition., Comment: 30 pages

In this paper, we give a systematic procedure for building locally stable dS vacua in $\mathcal{N}=1$ supergravity models motivated by string theory. We assume that one of the superfields has a Kahler potential of no-scale type and impose a hierarchy of supersymmetry breaking conditions. In the no-scale modulus direction the supersymmetry breaking is not small, in all other directions it is of order $\epsilon$. We establish the existence of an abundance of vacua for large regions in the parameter space spanned by $\epsilon$ and the cosmological constant. These regions exist regardless of the details of the other moduli, provided the superpotential can be tuned such that the off-diagonal blocks of the mass matrix are parametrically small. We test and support this general dS landscape construction by explicit analytic solutions for the STU model. The Minkowski limits of these dS vacua either break supersymmetry or have flat directions in agreement with a no-go theorem that we prove, stating that a supersymmetric Minkowski vacuum without flat directions cannot be continuously deformed into a non-supersymmetric vacuum. We also describe a method for finding a broad class of stable supersymmetric Minkowski vacua that can be F-term uplifted to dS vacua and which have an easily controllable SUSY breaking scale., Comment: 30 pages

Supergravity models of natural inflation and its generalizations are presented. These models are special examples of the class of supergravity models proposed in arXiv:1008.3375 and arXiv:1011.5945, which have a shift symmetric K\"ahler potential, superpotential linear in goldstino, and stable Minkowski vacua. We present a class of supergravity models with arbitrary potentials modulated by sinusoidal oscillations, similar to the potentials associated with axion monodromy models. We show that one can implement natural inflation in supergravity even in the models of a single axion field with axion parameters O(1). We also discuss the irrational axion landscape in supergravity, which describes a potential with infinite number of stable Minkowski and metastable dS minima., Comment: 5 pages, 4 figures. v2: references and figure added and landscape discussion extended, v3: minor changes, published version

We investigate the recently proposed possibility of chaotic inflation with respect to the imaginary part of the field T in a supersymmetric embedding of the Starobinsky model. We show that the stage of rapid expansion driven by Im T in this model ends almost instantly, and the subsequent stages of inflation are driven by the real part of the field T, as in the standard Starobinsky model. Thus, the Starobinsky model and its supersymmetric generalizations remain disfavored by the recent BICEP2 data., Comment: 10 pages, 6 figures, minor corrections

We present an analysis parallel to that of Giusto, Ross, and Saxena (arXiv:0708.3845) and construct a discrete family of non-supersymmetric microstate geometries of the Maldacena-Strominger-Witten system. The supergravity configuration in which we look for the smooth microstates is constructed using SO(4,4) dualities applied to an appropriate seed solution. The SO(4,4) approach offers certain technical advantages. Our microstate solutions are smooth in five dimensions, as opposed to all previously known non-supersymmetric microstates with AdS3 cores, which are smooth only in six dimensions. The decoupled geometries for our microstates are related to global AdS3 x S2 by spectral flows., Comment: 38 pages, including appendices and references; v2 refs + one paragraph added

Compactifications with D-brane and orientifold sources lead to standard gauged supergravity theories if the sources are smeared over the internal directions. It is therefore of interest to find how the solutions described by the gauged supergravity are altered by properly localising the sources. In this paper we analyse this for BPS domain wall solutions in the seven-dimensional gauged supergravity obtained from an O6 toroidal orientifold in massive IIA supergravity. This is one of the simplest no-scale supergravities that can be constructed and analysed in full detail. We find the BPS domain walls when the O6 planes are smeared. When the O6 planes are localised the domain wall solutions live in a warped compactification and we present the first-order equations these domain walls obey in 10 dimensions. In order to get explicit expressions we also consider the non-compact versions of the solutions for which the O6 planes have been traded for D6 branes and we recover the gauged supergravity expressions for the domain walls in the leading terms of the warp factor. Through T-duality we obtain partially localised solutions for compactifications to four dimensions using O3 planes with 3-form fluxes.

Compactifications with D-brane and orientifold sources lead to standard gauged supergravity theories if the sources are smeared over the internal directions. It is therefore of interest to find how the solutions described by the gauged supergravity are altered by properly localising the sources. In this paper we analyse this for BPS domain wall solutions in the seven-dimensional gauged supergravity obtained from an O6 toroidal orientifold in massive IIA supergravity. This is one of the simplest no-scale supergravities that can be constructed and analysed in full detail. We find the BPS domain walls when the O6 planes are smeared. When the O6 planes are localised the domain wall solutions live in a warped compactification and we present the first-order equations these domain walls obey in 10 dimensions. In order to get explicit expressions we also consider the non-compact versions of the solutions for which the O6 planes have been traded for D6 branes and we recover the gauged supergravity expressions for the domain walls in the leading terms of the warp factor. Through T-duality we obtain partially localised solutions for compactifications to four dimensions using O3 planes with 3-form fluxes.

Compactifications with D-brane and orientifold sources lead to standard gauged supergravity theories if the sources are smeared over the internal directions. It is therefore of interest to find how the solutions described by the gauged supergravity are altered by properly localising the sources. In this paper we analyse this for BPS domain wall solutions in the seven-dimensional gauged supergravity obtained from an O6 toroidal orientifold in massive IIA supergravity. This is one of the simplest no-scale supergravities that can be constructed and analysed in full detail. We find the BPS domain walls when the O6 planes are smeared. When the O6 planes are localised the domain wall solutions live in a warped compactification and we present the first-order equations these domain walls obey in 10 dimensions. In order to get explicit expressions we also consider the non-compact versions of the solutions for which the O6 planes have been traded for D6 branes and we recover the gauged supergravity expressions for the domain walls in the leading terms of the warp factor. Through T-duality we obtain partially localised solutions for compactifications to four dimensions using O3 planes with 3-form fluxes.

We investigate the recently proposed possibility of chaotic inflation with respect to the imaginary part of the field T in a supersymmetric embedding of the Starobinsky model. We show that the stage of rapid expansion driven by Im T in this model ends almost instantly, and the subsequent stages of inflation are driven by the real part of the field T, as in the standard Starobinsky model. Thus, the Starobinsky model and its supersymmetric generalizations remain disfavored by the recent BICEP2 data., Comment: 10 pages, 6 figures, minor corrections

Supergravity models of natural inflation and its generalizations are presented. These models are special examples of the class of supergravity models proposed in arXiv:1008.3375 and arXiv:1011.5945, which have a shift symmetric K\"ahler potential, superpotential linear in goldstino, and stable Minkowski vacua. We present a class of supergravity models with arbitrary potentials modulated by sinusoidal oscillations, similar to the potentials associated with axion monodromy models. We show that one can implement natural inflation in supergravity even in the models of a single axion field with axion parameters O(1). We also discuss the irrational axion landscape in supergravity, which describes a potential with infinite number of stable Minkowski and metastable dS minima., Comment: 5 pages, 4 figures. v2: references and figure added and landscape discussion extended, v3: minor changes, published version

In this paper, we give a systematic procedure for building locally stable dS vacua in $\mathcal{N}=1$ supergravity models motivated by string theory. We assume that one of the superfields has a Kahler potential of no-scale type and impose a hierarchy of supersymmetry breaking conditions. In the no-scale modulus direction the supersymmetry breaking is not small, in all other directions it is of order $\epsilon$. We establish the existence of an abundance of vacua for large regions in the parameter space spanned by $\epsilon$ and the cosmological constant. These regions exist regardless of the details of the other moduli, provided the superpotential can be tuned such that the off-diagonal blocks of the mass matrix are parametrically small. We test and support this general dS landscape construction by explicit analytic solutions for the STU model. The Minkowski limits of these dS vacua either break supersymmetry or have flat directions in agreement with a no-go theorem that we prove, stating that a supersymmetric Minkowski vacuum without flat directions cannot be continuously deformed into a non-supersymmetric vacuum. We also describe a method for finding a broad class of stable supersymmetric Minkowski vacua that can be F-term uplifted to dS vacua and which have an easily controllable SUSY breaking scale., Comment: 30 pages