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The Swampland Distance Conjecture (SDC) restricts the geodesic distances that scalars can traverse in effective field theories as they approach points at infinite distance in moduli space. We propose that, when applied to the subset of light fields in effective theories with scalar potentials, the SDC restricts the amount of non-geodesicity allowed for trajectories along valleys of the potential. This is necessary to ensure consistency of the SDC as a valid swampland criterium at any energy scale across the RG flow. We provide a simple description of this effect in moduli space of hyperbolic space type, and products thereof, and obtain critical trajectories which lead to maximum non-geodesicity compatible with the SDC. We recover and generalize these results by expressing the SDC as a new Convex Hull constraint on trajectories, characterizing towers by their scalar charge to mass ratio in analogy to the Scalar Weak Gravity Conjecture. We show that recent results on the asymptotic scalar potential of flux compatifications near infinity in moduli space precisely realize these critical amounts of non-geodesicity. Our results suggest that string theory flux compactifications lead to the most generic potentials allowing for maximum non-geodesicity of the potential valleys while respecting the SDC along them., 35 pages, 6 figures

Swampland criteria like the Weak Gravity Conjecture should not only apply to particles, but also to other lower-codimension charged objects in 4d EFTs like strings and membranes. However, the description of the latter is in general subtle due to their large backreaction effects. In the context of 4d $\mathcal{N}=1$ EFTs, we consider $\frac12$BPS strings and membranes which are fundamental, in the sense that they cannot be resolved within the EFT regime. We argue that, if interpreted from the EFT viewpoint, the 4d backreaction of these objects translates into a classical RG flow of their couplings. Constraints on the UV charges and tensions get then translated to constraints on the axionic kinetic terms and scalar potential of the EFT. This uncovers new relations among the Swampland Conjectures, which become interconnected by the physical properties of low-codimension objects. In particular, using that string RG flows describe infinite field distance limits, we show that the WGC for strings implies the Swampland Distance Conjecture. Similarly, WGC-saturating membranes generate a scalar potential satisfying the de Sitter Conjecture., 57 pages + appendices, 12 figures; v2: typos corrected

In any consistent effective field theory of quantum gravity limits of infinite field distance are expected to lead to the EFT breakdown due to the appearance of an infinite tower of light states, as predicted by the Distance Conjecture. We review the Distant Axionic String Conjecture, which proposes that any 4d EFT infinite-field-distance limit can be realized as an RG flow of a fundamental axionic string. The RG flow can be understood in terms of the 4d backreaction of such a string, and implies that it becomes tensionless towards the said limit. This property is understood as a shielding mechanism towards realizing an exact axionic symmetry, and it implies the breakdown of the EFT in a way that reproduces the Distance Conjecture. Motivated by string theory data we further propose the Integral Scaling Conjecture, which provides a specific relation between the string tension and the EFT maximal cut-off set by the infinite tower of states., Contribution to the CORFU2021 proceedings. 13 pages, 4 figures

We initiate the systematic study of flux scalar potentials and their vacua by using asymptotic Hodge theory. To begin with, we consider F-theory compactifications on Calabi-Yau fourfolds with four-form flux. We argue that a classifications of all scalar potentials can be performed when focusing on regions in the field space in which one or several fields are large and close to a boundary. To exemplify the constraints on such asymptotic flux compactifications, we explicitly determine this classification for situations in which two complex structure moduli are taken to be large. Our classification captures, for example, the weak string coupling limit and the large complex structure limit. We then show that none of these scalar potentials admits de Sitter vacua at parametric control, formulating a new no-go theorem valid beyond weak string coupling. We also check that the recently proposed asymptotic de Sitter conjecture is satisfied near any infinite distance boundary. Extending this strategy further, we generally identify the type of fluxes that induce an infinite series of Anti-de Sitter vacua, thereby generalizing the well-known Type IIA settings. Finally, we argue that also the large field dynamics of any axion in complex structure moduli space is universally constrained. Displacing such an axion by large field values will generally lead to severe backreaction effects destabilizing other directions., 67 pages, v2: renamed singularity types to more naturally structure enhancement patterns, typos fixed, minor clarifications and references added, v3: published version, typos fixed

We draw attention to a class of generalized global symmetries, which we call "Chern-Weil global symmetries," that arise ubiquitously in gauge theories. The Noether currents of these Chern-Weil global symmetries are given by wedge products of gauge field strengths, such as $F_2 \wedge H_3$ and $\text{tr}(F_2^2)$, and their conservation follows from Bianchi identities. As a result, they are not easy to break. However, it is widely believed that exact global symmetries are not allowed in a consistent theory of quantum gravity. As a result, any Chern-Weil global symmetry in a low-energy effective field theory must be either broken or gauged when the theory is coupled to gravity. In this paper, we explore the processes by which Chern-Weil symmetries may be broken or gauged in effective field theory and string theory. We will see that many familiar phenomena in string theory, such as axions, Chern-Simons terms, worldvolume degrees of freedom, and branes ending on or dissolving in other branes, can be interpreted as consequences of the absence of Chern-Weil symmetries in quantum gravity, suggesting that they might be general features of quantum gravity. We further discuss implications of breaking and gauging Chern-Weil symmetries for particle phenomenology and for boundary CFTs of AdS bulk theories. Chern-Weil global symmetries thus offer a unified framework for understanding many familiar aspects of quantum field theory and quantum gravity., Comment: 62 pages + appendices, 5 figures. v2: References added

We observe a direct relation between the existence of fundamental axionic strings, dubbed EFT strings, and infinite distance limits in 4d $\mathcal{N}=1$ EFTs coupled to gravity. The backreaction of EFT strings can be interpreted as RG flow of their couplings, and allows one to probe different regimes within the field space of the theory. We propose that any 4d EFT infinite distance limit can be realised as an EFT string flow. We show that along such limits the EFT string becomes asymptotically tensionless, and so the EFT eventually breaks down. This provides an upper bound for the maximal field range of an EFT with a finite cut-off, and reproduces the Swampland Distance Conjecture from a bottom-up perspective. Even if there are typically other towers of particles becoming light, we propose that the mass of the leading tower scales as $m^2\sim \mathcal{T}^w$ in Planck units, with $\mathcal{T}$ the EFT string tension and $w$ a positive integer. Our results hold even in the presence of a non-trivial potential, as long as its energy scale remains well below the cut-off. We check both proposals for large classes of 4d $\mathcal{N}=1$ string compactifications, finding that only the values $w=1,2,3$ are realised., Comment: 72 pages + appendices, 6 figures; v3: typos corrected

We view and provide further evidence for a number of Swampland criteria, including the Weak Gravity Conjecture, Distance Conjecture and bounds on the finiteness of the quantum gravity vacua from the prism of the finiteness of black hole entropy. Furthermore we propose that at least all of these Swampland statements may be more fundamentally a consequence of the finiteness of quantum gravity amplitudes., Comment: 1 figure, 23 pages + appendices

It is widely believed that consistent theories of quantum gravity satisfy two basic kinematic constraints: they are free from any global symmetry, and they contain a complete spectrum of gauge charges. For compact, abelian gauge groups, completeness follows from the absence of a 1-form global symmetry. However, this correspondence breaks down for more general gauge groups, where the breaking of the 1-form symmetry is insufficient to guarantee a complete spectrum. We show that the correspondence may be restored by broadening our notion of symmetry to include non-invertible topological operators, and prove that their absence is sufficient to guarantee a complete spectrum for any compact, possibly disconnected gauge group. In addition, we prove an analogous statement regarding the completeness of twist vortices: codimension-2 objects defined by a discrete holonomy around their worldvolume, such as cosmic strings in four dimensions. We discuss how this correspondence is modified in various, more general contexts, including non-compact gauge groups, Higgsing of gauge theories, and the addition of Chern-Simons terms. Finally, we discuss the implications of our results for the Swampland program, as well as the phenomenological implications of the existence of twist strings., Comment: 55 pages + references; 3 figures; v2: minor revisions and references added

We analyze the charge-to-mass structure of BPS states in general infinite-distance limits of $\mathcal{N}=2$ compactifications of Type IIB string theory on Calabi-Yau three-folds, and use the results to sharpen the formulation of the Swampland Conjectures in the presence of multiple gauge and scalar fields. We show that the BPS bound coincides with the black hole extremality bound in these infinite distance limits, and that the charge-to-mass vectors of the BPS states lie on degenerate ellipsoids with only two non-degenerate directions, regardless of the number of moduli or gauge fields. We provide the numerical value of the principal radii of the ellipsoid in terms of the classification of the singularity that is being approached. We use these findings to inform the Swampland Distance Conjecture, which states that a tower of states becomes exponentially light along geodesic trajectories towards infinite field distance. We place general bounds on the mass decay rate $\lambda$ of this tower in terms of the black hole extremality bound, which in our setup implies $\lambda \geq 1/\sqrt{6}$. We expect this framework to persist beyond $\mathcal{N}=2$ as long as a gauge coupling becomes small in the infinite field distance limit., Comment: 66 pages, 10 figures; v2: typos corrected, references added

We formulate a series of conjectures relating the geometry of conformal manifolds to the spectrum of local operators in conformal field theories in $d>2$ spacetime dimensions. We focus on conformal manifolds with limiting points at infinite distance with respect to the Zamolodchikov metric. Our central conjecture is that all theories at infinite distance possess an emergent higher-spin symmetry, generated by an infinite tower of currents whose anomalous dimensions vanish exponentially in the distance. Stated geometrically, the diameter of a non-compact conformal manifold must diverge logarithmically in the higher-spin gap. In the holographic context our conjectures are related to the Distance Conjecture in the swampland program. Interpreted gravitationally, they imply that approaching infinite distance in moduli space at fixed AdS radius, a tower of higher-spin fields becomes massless at an exponential rate that is bounded from below in Planck units. We discuss further implications for conformal manifolds of superconformal field theories in three and four dimensions., 22 pages. v3: fixed compiling error

A number of Swampland conjectures and in particular the Trans-Planckian Censorship Conjecture (TCC) suggest that de Sitter space is highly unstable if it exists at all. In this paper we construct effective theories of scalars rolling on potentials which are dual to a chain of short-lived dS spaces decaying from one to the next through a cascade of non-perturbative nucleation of bubbles. We find constraints on the effective potential resulting from various swampland criteria, including TCC, Weak Gravity Conjecture and Distance Conjecture. Surprisingly we find that TCC essentially incorporates all the other ones, and leads to a subclass of possible dual effective potentials. These results marginally rule out emergence of eternal inflation in the dual effective theory. We discuss some cosmological implications of our observations., Comment: 21 pages + appendices, 7 figures. v2: References added v3: References corrected

A bubble of nothing is a spacetime instability where a compact dimension collapses. After nucleation, it expands at the speed of light, leaving "nothing" behind. We argue that the topological and dynamical mechanisms which could protect a compactification against decay to nothing seem to be absent in string compactifications once supersymmetry is broken. The topological obstruction lies in a bordism group and, surprisingly, it can disappear even for a SUSY-compatible spin structure. As a proof of principle, we construct an explicit bubble of nothing for a $T^3$ with completely periodic (SUSY-compatible) spin structure in an Einstein dilaton Gauss-Bonnet theory, which arises in the low-energy limit of certain heterotic and type II flux compactifications. Without the topological protection, supersymmetric compactifications are purely stabilized by a Coleman-deLuccia mechanism, which relies on a certain local energy condition. This is violated in our example by the nonsupersymmetric GB term. In the presence of fluxes this energy condition gets modified and its violation might be related to the Weak Gravity Conjecture. We expect that our techniques can be used to construct a plethora of new bubbles of nothing in any setup where the low-energy bordism group vanishes, including type II compactifications on $CY_3$, AdS flux compactifications on 5-manifolds, and M-theory on 7-manifolds. This lends further evidence to the conjecture that any non-supersymmetric vacuum of quantum gravity is ultimately unstable., Comment: 87 pages + appendices (including a 16-page shortened version), 15 figures

We consider constraints on $D$-dimensional theories in $M_D$, $dS_D$ and $AdS_D$ backgrounds in the light of AdS swampland conjectures as applied to their compactification in a circle. In particular we consider the non-SUSY AdS instability conjecture and the AdS distance conjecture. For $M_D$ and $dS_D$ vacua the results may be summarized by a light fermion conjecture which states that in theories with $\Lambda_D\geq 0$ and a positive first non-vanishing supertrace $(-1)^{k+1}\text{Str} M^{2k}>0$, a surplus of light fermions with mass $m_f\lesssim \Lambda_D^{1/D}$ must be present. On the contrary, the cases of $M_D$ and $AdS_D$ can be made consistent with the mild but not the strong version of the AdS Distance conjecture, since the KK tower in the lower $d$-dim theory will scale as $m\lesssim \Lambda_d^{\alpha}$ with $\alpha=1/d$. The above constraints also suggest that the Standard Model of particle physics would be inconsistent in Minkowski space but consistent in dS if the lightest neutrino is Dirac and lighter than the cosmological constant scale., Comment: Minor corrections. References added

Journal of High Energy Physics 2016.5 (2016): 095 reproduced by permission of Scuola Internazionale Superiore di Studi Avanzati (SISSA), In string theory compactifications it is common to find an effective Lagrangian for the scalar fields with a non-canonical kinetic term. We study the effective action of the scalar position moduli of Type II Dp-branes. In many instances the kinetic terms are in fact modified by a term proportional to the scalar potential itself. This can be linked to the appearance of higher-dimensional supersymmetric operators correcting the Kahler potential. We identify the supersymmetric dimension-eight operators describing the α 0 corrections captured by the D-brane Dirac-Born-Infeld action. Our analysis then allows an embedding of the D-brane moduli effective action into an N = 1 supergravity formulation. The effects of the potential-dependent kinetic terms may be very important if one of the scalars is the inflaton, since they lead to a flattening of the scalar potential. We analyze this flattening effect in detail and compute its impact on the CMB observables for single-field inflation with monomial potentials, This work is partially supported by the grants FPA2012-32828 from the MINECO, the ERC Advanced Grant SPLE under contract ERC-2012-ADG-20120216-320421 and the grant SEV-2012-0249 of the “Centro de Excelencia Severo Ochoa” Programme. I.V. is supported by a grant from the Max Planck Society

It has been recently pointed out that the polarization BICEP2 results are consistent with the identification of an inflaton mass m \simeq 10^{13} GeV with the SUSY breaking scale in an MSSM with a fine-tuned SM Higgs. This identification leads to a Higgs mass m_h \simeq 126 GeV, consistent with LHC measurements. Here we propose that this naturally suggests to identify the inflaton with the heavy MSSM Higgs system. The fact that the extrapolated Higgs coupling lambda_{SM}\simeq 0 at scales below the Planck scale suggests the Higgs degrees of freedom could be associated to a Wilson line or D-brane position modulus in string theory. The Higgs system then has a shift symmetry and an N=2 structure which guarantees that its potential has an approximate quadratic chaotic inflation form. These moduli in string compactifications, being compact, allow for a trans-Planckian inflaton field range analogous to a version of monodromy inflation., Comment: 6 pages. Misprints corrected, references added

Recent BICEP2 results on CMB polarisation B-modes suggest a high value for the inflation scale $V_0^{1/4} \simeq 10^{16}$ GeV, giving experimental evidence for a physical scale in between the EW scale and the Planck mass. We propose that this new high scale could be interpreted as evidence for a high SUSY breaking scale $M_{ss}\simeq 10^{12}-10^{13}$ GeV. We show that such a large value for $M_{ss}$ is consistent with a Higgs mass around 126 GeV. We briefly discuss some possible particle physics implications of this assumption., Comment: 5 pages, 1 figure. v2: references added

Journal of High Energy Physics 2016.4 (2016): 020 reproduced by permission of Scuola Internazionale Superiore di Studi Avanzati (SISSA), The recently proposed relaxion models require extremely large trans-Planckian axion excursions as well as a potential explicitly violating the axion shift symmetry. The latter property is however inconsistent with the axion periodicity, which corresponds to a gauged discrete shift symmetry. A way to make things consistent is to use monodromy, i.e. both the axion and the potential parameters transform under the discrete shift symmetry. The structure is better described in terms of a 3-form field Cµνρ coupling to the SM Higgs through its field strength F4. The 4-form also couples linearly to the relaxion, in the Kaloper-Sorbo fashion. The extremely small relaxion-Higgs coupling arises in a see-saw fashion as g ≈ F4/f, with f being the axion decay constant. We discuss constraints on this type of constructions from membrane nucleation and the Weak Gravity Conjecture. The latter requires the existence of membranes, whose too fast nucleation could in principle drive the theory out of control, unless the cut-off scale is lowered. This allows to rule out the simplest models with the QCD axion as relaxion candidate on purely theoretical grounds. We also discuss possible avenues to embed this structure into string theory, This work is partially supported by the grants FPA2012-32828 from the MINECO, the ERC Advanced Grant SPLE under contract ERC-2012-ADG-20120216-320421 and the grant SEV-2012-0249 of the “Centro de Excelencia Severo Ochoa” Programme. M.M. is supported by a “La Caixa” Ph.D scholarship. I.V. is supported by a grant from the Max Planck Society

Journal of High Energy Physics 2015.8 (2015): 032 reproduced by permission of Scuola Internazionale Superiore di Studi Avanzati (SISSA), We discuss quantum gravitational effects in Einstein theory coupled to periodic axion scalars to analyze the viability of several proposals to achieve superplanckian axion periods (aka decay constants) and their possible application to large field inflation models. The effects we study correspond to the nucleation of euclidean gravitational instantons charged under the axion, and our results are essentially compatible with (but independent of) the Weak Gravity Conjecture, as follows: single axion theories with superplanckian periods contain gravitational instantons inducing sizable higher harmonics in the axion potential, which spoil superplanckian inflaton field range. A similar result holds for multiaxion models with lattice alignment (like the Kim-Nilles-Peloso model). Finally, theories with N axions can still achieve a moderately superplanckian periodicity (by a √ N factor) with no higher harmonics in the axion potential. The Weak Gravity Conjecture fails to hold in this case due to the absence of some instantons, which are forbidden by a discrete ZN gauge symmetry. Finally we discuss the realization of these instantons as euclidean D-branes in string compactifications, This work is partially supported by the grants FPA2012-32828 from the MINECO, the ERC Advanced Grant SPLE under contract ERC-2012-ADG-20120216-320421 and the grant SEV-2012-0249 of the “Centro de Excelencia Severo Ochoa” Programme. M.M. is supported by a “La Caixa” Ph.D scholarship. I.V. is supported through the FPU grant AP-2012-2690

We propose that inflation is driven by a (complex) neutral Higgs of the MSSM extension of the SM, in a chaotic-like inflation setting. The SUSY breaking soft term masses are of order $10^{12}-10^{13}$ GeV, which is identified with the inflaton mass scale and is just enough to stabilise the SM Higgs potential. The fine-tuned SM Higgs has then a mass around 126 GeV, in agreement with LHC results. We point out that the required large field excursions of chaotic inflation may be realised in string theory with the (complex) inflaton/Higgs identified with a continuous Wilson line or D-brane position. We show specific examples and study in detail a IIB orientifold with D7-branes at singularities, with SM gauge group and MSSM Higgs sector. In this case the inflaton/Higgs fields correspond to D7-brane positions along a two-torus transverse to them. Masses and monodromy are induced by closed string $G_3$ fluxes, and the inflaton potential can be computed directly from the DBI+CS action. We show how this action sums over Planck suppressed corrections, which amount to a field dependent rescaling of the inflaton fields, leading to a linear potential in the large field regime. We study the evolution of the two components of the Higgs/inflaton and compute the slow-roll parameters for purely adiabatic perturbations. For large regions of initial conditions slow roll inflation occurs and 50-60 efolds are obtained with r>0.07, testable in forthcoming experiments. Our scheme is economical in the sense that both EWSB and inflation originate in the same sector of the theory, all inflaton couplings are known and reheating occurs efficiently., 71 pages, 18 colour figures; typos corrected and added references

Journal of High Energy Physics 2016.1 (2016): 128 reproduced by permission of Scuola Internazionale Superiore di Studi Avanzati (SISSA), In Higgs-otic inflation a complex neutral scalar combination of the h0 and H0 MSSM Higgs fields plays the role of inflaton in a chaotic fashion. The potential is protected from large trans-Planckian corrections at large inflaton if the system is embedded in string theory so that the Higgs fields parametrize a D-brane position. The inflaton potential is then given by a DBI+CS D-brane action yielding an approximate linear behaviour at large field. The inflaton scalar potential is a 2-field model with specific non-canonical kinetic terms. Previous computations of the cosmological parameters (i.e. scalar and tensor perturbations) did not take into account the full 2-field character of the model, ignoring in particular the presence of isocurvature perturbations and their coupling to the adiabatic modes. It is well known that for generic 2-field potentials such effects may significantly alter the observational signatures of a given model. We perform a full analysis of adiabatic and isocurvature perturbations in the Higgs-otic 2-field model. We show that the predictivity of the model is increased compared to the adiabatic approximation. Isocurvature perturbations moderately feed back into adiabatic fluctuations. However, the isocurvature component is exponentially damped by the end of inflation. The tensor to scalar ratio varies in a region r = 0.08–0.12, consistent with combined Planck/BICEP results, We would like to thank F. Marchesano, A. Uranga and A. Westphal for useful discussions. We acknowledge the use of [70–76] in the development and debugging of our numerical methods. This work has been supported by the ERC Advanced Grant SPLE under contract ERC-2012-ADG-20120216-320421, by the grant FPA2012-32828 from the MINECO, and the grant SEV-2012-0249 of the “Centro de Excelencia Severo Ochoa” Programme. I.V. is supported through the FPU grant AP-2012-2690

Closed string fluxes induce generically SUSY-breaking soft terms on supersymmetric type IIB orientifold compactifications with D3/D7 branes. This was studied in the past by inserting those fluxes on the DBI+CS actions for adjoint D3/D7 fields, where D7-branes had no magnetic fluxes. In the present work we generalise those computations to the phenomenologically more relevant case of chiral bi-fundamental fields laying at 7-brane intersections and F-theory local matter curves. We also include the effect of 7-brane magnetic flux as well as more general closed string backgrounds, including the effect of distant (anti-)D3-branes. We discuss several applications of our results. We find that squark/slepton masses become in general flux-dependent in F-theory GUT's. Hypercharge-dependent non-universal scalar masses with a characteristic sfermion hierarchy m_E^2 < m_L^2 < m_Q^2 < m_D^2 < m_U^2 are obtained. There are also flavor-violating soft terms both for matter fields living at intersecting 7-branes or on D3-branes at singularities. They point at a very heavy sfermion spectrum to avoid FCNC constraints. We also discuss the possible microscopic description of the fine-tuning of the EW Higgs boson in compactifications with a MSSM spectrum., 67 pages, 2 figures, 2 tables

We argue that in large classes of string compactifications with a MSSM-like structure substantial flavor violating SUSY-breaking soft terms are generically induced. We specify to the case of flavor dependent soft-terms in type IIB/F-theory SU(5) unified models, although our results can be easily extended to other settings. The Standard Model (SM) degrees of freedom reside in a local system of 7-branes wrapping a 4-fold S in the extra dimensions. It is known that in the presence of closed string 3-form fluxes SUSY-breaking terms are typically generated. We explore the generation dependence of these soft terms and find that non-universalities arise whenever the flux varies over the 4-fold S. These non-universalities are parametrically suppressed by (M_{GUT}/M_{Pl})^{1/3}. They also arise in the case of varying open string fluxes, in this case parametrically suppressed by \alpha_{GUT}^{1/2}. For a standard unification scheme with M_{GUT} = 10^{16} GeV and \alpha_{\rm GUT} = 1/24 these suppressions are very mild. Although limits from the kaon mass difference \Delta m_K are easily obeyed for squark masses above the present LHC limits, constraints from the CP-violation parameter \epsilon_K imply squark masses in the multi-TeV region. The constraints from BR(\mu \rightarrow e\gamma) turn out to be the strongest ones, with slepton masses of order ~10 TeV or heavier required to obey the experimental limits. These sfermion masses are consistent with the observed large value m_H ~ 126 GeV of the Higgs mass. We discuss under what conditions such strong limits may be relaxed allowing for SUSY particle production at LHC., Comment: 38 pages, 6 figures, 1 table; v2: references added

We compute the mass of the Higgs particle in a scheme in which SUSY is broken at a large scale M_{SS} well above the electroweak scale M_{EW}. Below M_{SS} one assumes one is just left with the SM with a fine-tuned Higgs potential. Under standard unification assumptions one can compute the mass of the Higgs particle as a function of the SUSY breaking scale M_{SS}. For M_{SS} > 10^{10} GeV one obtains m_H=126 \pm 3 GeV, consistent with CMS and ATLAS results. For lower values of M_{SS} the values of the Higgs mass tend to those of a fine-tuned MSSM with m_H < 130 GeV. These results support the idea that the measured value of the Higgs mass at LHC may be considered as indirect evidence for the existence of SUSY at some (not necessarily low) mass scale., 25 pages, 7 figures. Slight changes in figures. Conclusions unchanged

We study the phenomenological viability of a constrained NMSSM with parameters subject to unified boundary conditions from F-theory GUTs. We find that very simple assumptions about modulus dominance SUSY breaking in F-theory unification lead to a predictive set of boundary conditions, consistent with all phenomenological constraints. The second lightest scalar Higgs H_2 can get a mass m_{H_2} ~ 125 GeV and has properties similar to the SM Higgs. On the other hand the lightest scalar H_1, with a dominant singlet component, would have barely escaped detection at LEP and could be observable at LHC as a peak in H_1 -> gamma gamma at around 100 GeV. The LSP is mostly singlino and is consistent with WMAP constraints due to coannihilation with the lightest stau, whose mass is in the range 100-250 GeV. Such light staus may lead to very characteristic signatures at LHC and be directly searched at linear colliders. In these models tan(beta) is large, of order 50, still the branching ratio for B_s -> mu+ mu- is consistent with the LHCb bounds and in many cases is also even smaller than the SM prediction. Gluinos and squarks have masses in the 2 - 3 TeV region and may be accessible at the LHC at 14 TeV. No large enhancement of the H_2 -> gamma gamma rate over that of the SM Higgs is expected., 46 pages, 13 figures. Typo in Table 4 corrected