Search

We investigate the charging dynamics of Sachdev-Ye-Kitaev (SYK) models as quantum batteries, highlighting their capacity to achieve quantum charging advantages. By analytically deriving the scaling of the charging power in SYK batteries, we identify the two key mechanisms underlying this advantage: the use of operators scaling extensively with system size $N$ and the facilitation of operator delocalization by specific graph structures. A novel graph-theoretic framework is introduced in which the charging process is recast as a random walk on a graph, enabling a quantitative analysis of operator spreading. Our results establish rigorous conditions for the quantum advantage in SYK batteries and extend these insights to graph-based SYK models, revealing broader implications for energy storage and quantum dynamics. This work opens avenues for leveraging quantum chaos and complex network structures in optimizing energy transfer processes., Comment: 9 pages, 4 figures

We present numerical results for the Rosenzweig Porter model for all symmetry classes of the Dyson threefold way. We analyzed the fluctuation properties in the eigenvalue spectra, and compared them with existing and new analytical results. Based on these results we propose characteristics of the spectral properties as measures to explore the transition from Poisson to Wigner Dyson WD statistics. Furthermore, we performed thorough studies of the properties of the eigenvectors in terms of the fractal dimensions, the Kullback Leibler KL divergences and the fidelity susceptibility. The ergodic and Anderson transitions take place at the same parameter values and a finite size scaling analysis of the KL divergences at the transitions yields the same critical exponents for all three WD classes, thus indicating superuniversality of these transitions.

We present a detailed study of an asymmetrically driven quantum Otto engine with a time-dependent harmonic oscillator as its working medium. We obtain analytic expressions for the upper bounds on the efficiency of the engine for two different driving schemes having asymmetry in the expansion and compression work strokes. We show that the Otto cycle under consideration cannot operate as a heat engine in the low-temperature regime. Then, we show that the friction in the expansion stroke is significantly more detrimental to the performance of the engine as compared to the friction in the compression stroke. Further, by comparing the performance of the engine with sudden expansion, sudden compression, and both sudden strokes, we uncover a pattern of connections between the operational points, and we indicate the optimal operation regime for each case. Finally, we analytically characterize the complete phase diagram of the Otto cycle for both driving schemes and highlight the different operational modes of the cycle as a heat engine, refrigerator, accelerator, and heater.

We introduce a quantum charging distance as the minimal time that it takes to reach one state (charged state) from another state (depleted state) via a unitary evolution, assuming limits on the resources invested into the driving Hamiltonian. For pure states it is equal to the Bures angle, while for mixed states, its computation leads to an optimization problem. Thus, we also derive easily computable bounds on this quantity. The charging distance tightens the known bound on the mean charging power of a quantum battery, it quantifies the quantum charging advantage, and it leads to an always achievable quantum speed limit. In contrast with other similar quantities, the charging distance does not depend on the eigenvalues of the density matrix, it depends only on the corresponding eigenspaces. This research formalizes and interprets quantum charging in a geometric way, and provides a measurable quantity that one can optimize for to maximize the speed of charging of future quantum batteries., Comment: 15 pages, 4 figures, v2: added Table I: main results, extended discussion on the quantum speed limit

We demonstrate that an image recognition algorithm based on a convolutional neural network provides a powerful procedure to differentiate between ergodic, non-ergodic extended (fractal) and localized phases in various systems: single-particle models, including random-matrix and random-graph models, and many-body quantum systems. The network can be successfully trained on a small data set of only 500 wave functions (images) per class for a single model. The trained network can then be used to classify phases in the other models and is thus very efficient. We discuss the strengths and limitations of the approach., Comment: 9 pages, 10 figures + 2 pages, 4 figures, 1 table in appendices

The generation of a large amount of entanglement is a necessary condition for a quantum computer to achieve quantum advantage. In this paper, we propose a method to efficiently generate pseudo-random quantum states, for which the degree of multipartite entanglement is nearly maximal. We argue that the method is optimal, and use it to benchmark actual superconducting (IBM's ibm_lagos) and ion trap (IonQ's Harmony) quantum processors. Despite the fact that ibm_lagos has lower single-qubit and two-qubit error rates, the overall performance of Harmony is better thanks to low error rate in state preparation and measurement and to the all-to-all connectivity of qubits. Our result highlights the relevance of the qubits network architecture to generate highly entangled state., Comment: 14 pages, 8 figures

Understanding the mechanisms underlying many-body quantum chaos is one of the big challenges in theoretical physics. We tackle this problem by considering a set of perturbed quadratic Sachdev-Ye-Kitaev (SYK) Hamiltonians defined on graphs. This allows to disambiguate between operator growth and \emph{delocalization}, showing that the latter is the dominant process in the single-particle to many-body chaotic transition. Our results are verified numerically with state-of-the-art numerical techniques, capable of extracting eigenvalues in a desired energy window of very large Hamiltonians, in this case up to dimension $2^{19}\times 2^{19}$. Our approach essentially provides a new way of viewing many-body chaos from a single-particle perspective., Comment: 5 + 1 pages, 4 + 1 figures

We present a method to estimate the probabilities of outcomes of a quantum observable, its mean value, and higher moments by measuring any other observable. This method is general and can be applied to any quantum system. In the case of estimating the mean energy of an isolated system, the estimate can be further improved by measuring the other observable at different times. Intuitively, this method uses interplay and correlations between the measured observable, the estimated observable, and the state of the system. We provide two bounds: one that is looser but analytically computable and one that is tighter but requires solving a non-convex optimization problem. The method can be used to estimate expectation values and related quantities such as temperature and work in setups where performing measurements in a highly entangled basis is difficult, finding use in state-of-the-art quantum simulators. As a demonstration, we show that in Heisenberg and Ising models of ten sites in the localized phase, performing two-qubit measurements excludes 97.5% and 96.7% of the possible range of energies, respectively, when estimating the ground state energy., Comment: 7+9 pages, 6 figures, 3 tables. v2: significantly reworked structure and made it easier to read. Proofs simplified and moved to the main text. v3: title changed, cosmetic changes. Questions and comments are welcome

We propose a general computational framework for optimizing model-dependent parameters in quantum batteries (QB). We apply this method to two different charging scenarios in the micromaser QB and we discover a new charging protocol for stabilizing the battery in upper-laying Hilbert space chambers in a controlled and automatic way. This protocol is found to be stable and robust, and it leads to an improved charging efficiency in micromaser QBs. Moreover, our optimization framework is highly versatile and efficient, holding great promise for the advancement of QB technologies at all scales., Comment: 15 pages, 7 figures

We consider a micromaser model of a quantum battery, where the battery is a single mode of the electromagnetic field in a cavity, charged via repeated interactions with a stream of qubits, all prepared in the same non-equilibrium state, either incoherent or coherent, with the matter-field interaction modeled by the Jaynes-Cummings model. We show that the coherent protocol is superior to the incoherent one, in that an effective pure steady state is achieved for generic values of the model parameters. Finally, we supplement the above collision model with cavity losses, described by a Lindblad master equation. We show that battery performances, in terms of stored energy, charging power, and steady-state purity, are slightly degraded up to moderated dissipation rate. Our results show that micromasers are robust and reliable quantum batteries, thus making them a promising model for experimental implementations., Comment: 15 pages, 7 figures

We study the dynamical generation of entanglement for a two-body interacting system, starting from a separable coherent state. We show analytically that in the quasiclassical regime the entanglement growth rate can be simply computed by means of the underlying classical dynamics. Furthermore, this rate is given by the Kolmogorov-Sinai entropy, which characterizes dynamical complexity of classical motion. Our results, illustrated by numerical simulations on a model of coupled rotators, establish in the quasiclassical regime a link between the generation of entanglement, a purely quantum phenomenon, and classical complexity., Comment: 10 pages. 3 figures

We investigate the thermodynamic uncertainty relation (TUR), \textit{i.e.} a trade-off between entropy production rate and relative power fluctuations, for nondegenerate three-level and degenerate four-level maser heat engines. In the nondegenerate case, we consider two slightly different configurations of three-level maser heat engine and contrast their degree of violation of standard TUR. In the high-temperature limit, standard TUR relation is always violated for both configurations. We also uncover an invariance of TUR under simultaneous rescaling of the matter-field coupling constant and system-bath coupling constants. For the degenerate four level engine, we study the effects of noise-induced coherence on TUR. We show that depending on the parametric regime of operation, noise-induced coherence can either suppress or enhance the relative power fluctuations., Comment: 12 pages, 5 figures

Energy extraction is a central task in thermodynamics. In quantum physics, ergotropy measures the amount of work extractable under cyclic Hamiltonian control. As its full extraction requires perfect knowledge of the initial state, however, it does not characterize the work value of unknown or untrusted quantum sources. Fully characterizing such sources would require quantum tomography, which is prohibitively costly in experiments due to the exponential growth of required measurements and operational limitations. Here, we therefore derive a new notion of ergotropy applicable when nothing is known about the quantum states produced by the source, apart from what can be learned by performing only a single type of coarse-grained measurement. We find that in this case the extracted work is defined by the Boltzmann and observational entropy, in cases where the measurement outcomes are, or are not, used in the work extraction, respectively. This notion of ergotropy represents a realistic measure of extractable work, which can be used as the relevant figure of merit to characterize a quantum battery., Comment: 5+1(Appendix)+7(Supplemental) pages, 4 figures. Comments and questions welcome. v2: changed the interpretation of the coarse-grained extraction operations (former eq (6), now eq (7)). Appendix with examples added. Results unchanged. v3: technical details moved into a short appendix. Added explanatory figure for the extraction operations. Added extra proof in the Supplemental Material

We study the thermalizing properties of the mass-deformed SYK model, in a regime of parameters where the eigenstates are ergodically extended over just portions of the full Fock space, as an all-to-all toy model of many-body localization. Our numerical results strongly support the hypothesis that, although considerably delayed, thermalization is still present in this regime. Our results add to recent studies indicating that many-body localization should be interpreted as a strict Fock-space localization., Comment: 9 pages, 6 figures

We show that a micromaser is an excellent model of quantum battery. A highly excited, pure, and effectively steady state of the cavity mode, charged by coherent qubits, can be achieved, also in the ultrastrong coupling regime of field-matter interaction. Stability of these appealing features against loss of coherence of the qubits and the effect of counter-rotating terms in the interaction Hamiltonian are also discussed., Comment: 6 pages, 1 figure

Recent studies have revealed intriguing similarities between the contribution of wormholes to the gravitational path integral and the phenomenon of replica symmetry breaking observed in spin glasses and other disordered systems. Interestingly, these configurations may also be important for the explanation of the information paradox of quantum black holes. Motivated by these developments, we investigate the thermodynamic properties of a $PT$-symmetric system composed of two random non-Hermitian Hamiltonians with no explicit coupling between them. After performing ensemble averaging, we identify numerically and analytically a robust first-order phase transition in the free energy of two models with quantum chaotic dynamics: the elliptic Ginibre ensemble of random matrices and a non-Hermitian Sachdev-Ye-Kitaev (SYK) model. The free energy of the Ginibre model is temperature-independent in the low-temperature phase. The SYK model has a similar behavior for sufficiently low temperature, then it experiences a possible continuous phase transition to a phase with a temperature-dependent free energy before the first-order transition takes place at a higher temperature. We identify the order parameter of the first-order phase transition and obtain analytical expressions for the critical temperature. The mechanism behind the transition is the existence of replica symmetry breaking configurations coupling Left and Right replicas that control the low-temperature limit of the partition function. We speculate that quantum chaos may be necessary for the observed dominance of off-diagonal replica symmetry breaking configurations in the low-temperature limit., Comment: 44+20 pages. Some of the results of this paper were announced in arxiv:2102:06630 (Phys.Rev.Lett. 128 (2022) 8, 081601)

We analyze a two-body nonhermitian two-site Sachdev-Ye-Kitaev model with the couplings of one site complex conjugated to the other site. This model, with no explicit coupling between the sites, shows an infinite number of phase transitions which is a consequence of the partition function factorizing into a product over Matsubara frequencies. We calculate the quenched free energy in two different ways, first in terms of the single-particle energies, and second by solving the Schwinger-Dyson equations. The first calculation can be done entirely in terms of a one-site model. The conjugate replica enters due to non-analyticities when Matsubara frequencies enter the spectral support of the coupling matrix. The second calculation is based on the replica trick of the two-site partition function. Both methods give the same result. The free-fermion partition function can be rephrased as a matrix model for the coupling matrix. Up to minor details, this model is the random matrix model that describes the chiral phase transition of QCD, and the order parameter of the two-body model corresponds to the chiral condensate of QCD. Comparing to the corresponding four-body model, we are able to determine which features of the free energy are due to chaotic nature of the four-body model. The high-temperature phase of both models is entropy dominated, and in both cases is determined by the spectral density. The four-body SYK model has a low-temperature phase whose free energy is almost temperature-independent, signaling an effective gap of the theory even though the actual spectrum does not exhibit a gap. However the low-temperature free energy of the two-body SYK model is not flat, in fact it oscillates to arbitrarily low temperature. This indicates a less desirable feature that the entropy of the two-body model is not always positive, which most likely is a consequence of the nonhermiticity., Comment: To be submitted to the Dyson memorial volume of the Journal of Mathematical Physics

We explore quantum chaos diagnostics of variational circuit states at random parameters and study their correlation with the circuit expressibility and the optimization of control parameters. By measuring the operator spreading coefficient and the eigenvalue spectrum of the modular Hamiltonian of the reduced density matrix, we identify the universal structure of random matrix models in high-depth circuit states. We construct different layer unitaries corresponding to the GOE and GUE distributions and quantify their VQA performance. Our study also highlights a potential tension between the OTOC and BGS-type diagnostics of quantum chaos., Comment: 12 pages, 10 figures

We investigate the delocalization of operators in non-chaotic quantum systems whose interactions are encoded in an underlying graph or network. In particular, we study how fast operators of different sizes delocalize as the network connectivity is varied. We argue that these delocalization properties are well captured by Krylov complexity and show, numerically, that efficient delocalization of large operators can only happen within sufficiently connected network topologies. Finally, we demonstrate how this can be used to furnish a deeper understanding of the quantum charging advantage of a class of SYK-like quantum batteries., Comment: Main document: 6 pages, 3 figures. Supplemental material: 8 pages, 3 figures

We show that a neural network, trained on the entanglement spectra of a nearest neighbor Heisenberg chain in a random transverse magnetic field, can be used to efficiently study the ergodic/many-body localized properties of a number of other quantum systems, without further re-training. We benchmark our computational architecture against a $J_{1}\!\!-\!\!J_{2}$ - model, which extends the Heisenberg chain to include next-to-nearest neighbor interactions, with excellent agreement with known results. When applied to Hamiltonians that differ from the training model by the topology of the underlying graph, the neural network is able to predict the critical disorders and, more generally, shapes of the mobility edge that agree with our heuristic expectation. We take this as proof of principle that machine learning algorithms furnish a powerful new set of computational tools to explore the many-body physics frontier., Comment: Main text: 6 pages, 3 figures. Supplementary material: 4 pages, 3 figures

Quantum batteries are devices made from quantum states, which store and release energy in a fast and efficient manner, thus offering numerous possibilities in future technological applications. They offer a significant charging speedup when compared to classical batteries, due to the possibility of using entangling charging operations. We show that the maximal speedup that can be achieved is extensive in the number of cells, thus offering at most quadratic scaling in the charging power over the classically achievable linear scaling. To reach such a scaling, a global charging protocol, charging all the cells collectively, needs to be employed. This concludes the quest on the limits of charging power of quantum batteries and adds to other results in which quantum methods are known to provide at most quadratic scaling over their classical counterparts., Comment: Main text: 5 pages, 1 figure. Supplemental material: 7 pages, 3 figures: v2: main: extended explanation of the source of the quantum advantage and comparison with parallel charging, references added, and other minor changes. Supplemental material: additional discussion of the scaling of the bandwidth of Fig. 1

We show that the low temperature phase of a conjugate pair of uncoupled, quantum chaotic, nonhermitian systems such as the Sachdev-Ye-Kitaev (SYK) model or the Ginibre ensemble of random matrices are dominated by replica symmetry breaking configurations with a nearly flat free energy that terminates in a first order phase transition. In the case of the SYK model, we show explicitly that the spectrum of the effective replica theory has a gap. These features are strikingly similar to those induced by wormholes in the gravity path integral which suggests a close relation between both configurations. For a non-chaotic SYK, the results are qualitatively different: the spectrum is gapless in the low temperature phase and there is an infinite number of second order phase transitions unrelated to the restoration of replica symmetry., Comment: References added, typos corrected

We explore the effectiveness of variational quantum circuits in simulating the ground states of quantum many-body Hamiltonians. We show that generic high-depth circuits, performing a sequence of layer unitaries of the same form, can accurately approximate the desired states. We demonstrate their universal success by using two Hamiltonian systems with very different properties: the transverse field Ising model and the Sachdev-Ye-Kitaev model. The energy landscape of the high-depth circuits has a proper structure for the gradient-based optimization, i.e. the presence of local extrema -- near any random initial points -- reaching the ground level energy. We further test the circuit's capability of replicating random quantum states by minimizing the Euclidean distance., Comment: v1: revtex4-1, 14 pages, 11 figures; v2: 13 pages, revised for journal submission

We study a sparse Sachdev-Ye-Kitaev (SYK) model with $N$ Majoranas where only $\sim k N$ independent matrix elements are non-zero. We identify a minimum $k \gtrsim 1$ for quantum chaos to occur by a level statistics analysis. The spectral density in this region, and for a larger $k$, is still given by the Schwarzian prediction of the dense SYK model, though with renormalized parameters. Similar results are obtained for a beyond linear scaling with $N$ of the number of non-zero matrix elements. This is a strong indication that this is the minimum connectivity for the sparse SYK model to still have a quantum gravity dual. We also find an intriguing exact relation between the leading correction to moments of the spectral density due to sparsity and the leading $1/d$ correction of Parisi's U(1) lattice gauge theory in a $d$ dimensional hypercube. In the $k \to 1$ limit, different disorder realizations of the sparse SYK model show emergent random matrix statistics that for fixed $N$ can be in any universality class of the ten-fold way. The agreement with random matrix statistics is restricted to short range correlations, no more than a few level spacings, in particular in the tail of the spectrum. In addition, emergent discrete global symmetries in most of the disorder realizations for $k$ slightly below one give rise to $2^m$-fold degenerate spectra, with $m$ being a positive integer. For $k =3/4$, we observe a large number of such emergent global symmetries with a maximum $2^8$-fold degenerate spectra for $N = 26$., Comment: 48 pages, 26 figures

We study non-equilibrium dynamics induced by a sudden quench of strongly correlated Hamiltonians with all-to-all interactions. By relying on a Sachdev-Ye-Kitaev (SYK) based quench protocol, we show that the time evolution of simple spin-spin correlation functions is highly sensitive to the degree of locality of the corresponding operators, once an appropriate set of fundamental fields is identified. By tracking the time-evolution of specific spin-spin correlation functions and their decay, we argue that it is possible to distinguish between operator hopping and operator growth dynamics; the latter being a hallmark of quantum chaos in many-body quantum systems. Such observation, in turn, could constitute a promising tool to probe the emergence of chaotic behavior, rather accessible in state-of-the-art quench setups., Comment: v2: Fixed broken Unicode characters; REVTeX4-1, 13 pages, 14 figures

The exactly-solvable Sachdev-Ye-Kitaev (SYK) model has recently received considerable attention in both condensed matter and high energy physics because it describes quantum matter without quasiparticles, while being at the same time the holographic dual of a quantum black hole. In this Letter, we examine SYK-based charging protocols of quantum batteries with N quantum cells. Extensive numerical calculations based on exact diagonalization for N up to 16 strongly suggest that the optimal charging power of our SYK quantum batteries displays a super-extensive scaling with N that stems from genuine quantum mechanical effects. While the complexity of the nonequilibrium SYK problem involved in the charging dynamics prevents us from an analytical proof, we believe that this Letter offers the first (to the best of our knowledge) strong numerical evidence of a quantum advantage occurring due to the maximally-entangling underlying quantum dynamics., Comment: 12 pages, 7 figures. Final version

Collective behavior strongly influences the charging dynamics of quantum batteries (QBs). Here, we study the impact of nonlocal correlations on the energy stored in a system of $N$ QBs. A unitary charging protocol based on a Sachdev-Ye-Kitaev (SYK) quench Hamiltonian is thus introduced and analyzed. SYK models describe strongly interacting systems with nonlocal correlations and fast thermalization properties. Here, we demonstrate that, once charged, the average energy stored in the QB is very stable, realizing an ultraprecise charging protocol. By studying fluctuations of the average energy stored, we show that temporal fluctuations are strongly suppressed by the presence of nonlocal correlations at all time scales. A comparison with other paradigmatic examples of many-body QBs shows that this is linked to the collective dynamics of the SYK model and its high level of entanglement. We argue that such feature relies on the fast scrambling property of the SYK Hamiltonian, and on its fast thermalization properties, promoting this as an ideal model for the ultimate temporal stability of a generic QB. Finally, we show that the temporal evolution of the ergotropy, a quantity that characterizes the amount of extractable work from a QB, can be a useful probe to infer the thermalization properties of a many-body quantum system., Comment: 13 pages, 11 figures; v2: references added; a new section discussing the role of quantum chaos added; version to appear on JHEP

It has been recently proposed by Maldacena and Qi that an eternal traversable wormhole in a two dimensional Anti de Sitter space (${\rm AdS}_2$) is the gravity dual of the low temperature limit of two Sachdev-Ye-Kitaev (SYK) models coupled by a relevant interaction (which we will refer to as spin operator). In this paper, we study spectral and eigenstate properties of this coupled SYK model. We have found that level statistics in the tail of the spectrum, and for a sufficiently weak coupling, shows substantial deviations from random matrix theory which suggests that traversable wormholes are not quantum chaotic. By contrast, for sufficiently strong coupling, corresponding to the black hole phase, level statistics are well described by random matrix theory. This transition in level statistics coincides approximately with a previously reported Hawking-Page transition for weak coupling. We have shown explicitly that this thermodynamic transition turns into a sharp crossover as the coupling increases. Likewise, this critical coupling also corresponds with the one at which the overlap between the ground state and the thermofield double state (TFD) is smallest. In the range of sizes we can reach by exact diagonalization, the ground state is well approximated by the TFD state only in the strong coupling limit. This is due to the fact that the ground state is close to the eigenstate of the spin operator corresponding to the lowest eigenvalue which is an exact TFD state at infinite temperature. In this region, the spectral density is separated into blobs centered around the eigenvalues of the spin operator. For weaker couplings, the exponential decay of coefficients in a tensor product basis, typical of the TFD, becomes power law. Finally, we have also found that the total Hamiltonian has an additional discrete symmetry which has not been reported previously., Comment: References added, typos corrected

We study the onset of RMT dynamics in the mass-deformed SYK model (i.e. an SYK model deformed by a quadratic random interaction) in terms of the strength of the quadratic deformation. We use as chaos probes both the connected unfolded Spectral Form Factor (SFF) as well as the Gaussian-filtered SFF, which has been recently introduced in the literature. We show that they detect the chaotic/integrable transition of the mass-deformed SYK model at different values of the mass deformation: the Gaussian-filtered SFF sees the transition for large values of the mass deformation; the connected unfolded SFF sees the transition at small values. The latter is in qualitative agreement with the transition as seen by the OTOCs. We argue that the chaotic/integrable deformation affect the energy levels inhomogeneously: for small values of the mass deformation only the low-lying states are modified while for large values of the mass deformation also the states in the bulk of the spectrum move to the integrable behavior., Comment: 44 pages, many figures

We review the topological structure, sitting in any supergravity theory, which has been recently discovered in arXiv: 1801.04940. We describe how such a structure allows for a cohomological reformulation of the generalized Killing spinor equations which characterize bosonic supergravity solutions with unbroken supersymmetry., Comment: 8 pages, proceedings paper for the 10-th International Symposium "Quantum Theory and Symmetries" (QTS10)

The BRST algebra of supergravity is characterized by two different bilinears of the commuting supersymmetry ghosts: a vector $\gamma^\mu$ and a scalar $\phi$, the latter valued in the Yang-Mills Lie algebra. We observe that under BRST transformations $\gamma$ and $\phi$ transform as the superghosts of, respectively, topological gravity and topological Yang-Mills coupled to topological gravity. This topological structure sitting inside any supergravity leads to universal equivariant cohomological equations for the curvatures 2-forms which hold on supersymmetric bosonic backgrounds. Additional equivariant cohomological equations can be derived for supersymmetric backgrounds of supergravities for which certain gauge invariant scalar bilinears of the commuting ghosts exist. Among those, $N= (2,2)$ in $d=2$, which we discuss in detail in this paper, and $N=2$ in $d=4$., Comment: 38 pages

We contrast some aspects of various SYK-like models with large-$N$ melonic behavior. First, we note that ungauged tensor models can exhibit symmetry breaking, even though these are 0+1 dimensional theories. Related to this, we show that when gauged, some of them admit no singlets, and are anomalous. The uncolored Majorana tensor model with even $N$ is a simple case where gauge singlets can exist in the spectrum. We outline a strategy for solving for the singlet spectrum, taking advantage of the results in arXiv:1706.05364, and reproduce the singlet states expected in $N=2$. In the second part of the paper, we contrast the random matrix aspects of some ungauged tensor models, the original SYK model, and a model due to Gross and Rosenhaus. The latter, even though disorder averaged, shows parallels with the Gurau-Witten model. In particular, the two models fall into identical Andreev ensembles as a function of $N$. In an appendix, we contrast the (expected) spectra of AdS$_2$ quantum gravity, SYK and SYK-like tensor models, and the zeros of the Riemann Zeta function., Comment: 45 pages, 17 figures; v2: minor improvements and rearrangements, refs added

We extend the coupling to the topological backgrounds, recently worked out for the 2-dimensional BF-model, to the most general Poisson sigma models. The coupling involves the choice of a Casimir function on the target manifold and modifies the BRST transformations. This in turn induces a change in the BRST cohomology of the resulting theory. The observables of the coupled theory are analyzed and their geometrical interpretation is given. We finally couple the theory to 2-dimensional topological gravity: this is the first step to study a topological string theory in propagation on a Poisson manifold. As an application, we show that the gauge-fixed vectorial supersymmetry of the Poisson sigma models has a natural explanation in terms of the theory coupled to topological gravity., Comment: 31 pages; v2: typos fixed, references added, version to appear in JHEP

Supersymmetric field theories can be studied exactly on suitable off-shell supergravity backgrounds. We show that in two dimensions such backgrounds are identifiable with BRST invariant backgrounds of topological gravity coupled to an abelian topological gauge multiplet. This latter background is required for the consistent coupling of the topological `matter' YM theory to topological gravity. We make use of this topological point of view to obtain, in a simple and straightforward way, a complete classification of localizing supersymmetric backgrounds in two dimensions. The BRST invariant topological backgrounds are parametrized by both Killing vectors and $S^1$-equivariant cohomology of the 2-dimensional world-sheet. We reconstruct completely the supergravity backgrounds from the topological data: some of the supergravity fields are twisted versions of the topological backgrounds, but others are "composite", i.e. they are non-linear functionals of them. We recover all the known localizing 2-dimensional backgrounds and (infinitely) many more that have not been explored so far. We show that the supersymmetric $\Omega$-deformation is nothing but the background value of the ghost-for-ghost of topological gravity, a result which holds for other dimensions too. The new localizing backgrounds are characterized by non-trivial fluxes for both the graviphotons of the supergravity multiplet., Comment: 45 pages, 2 figures, revised introduction, version published on JHEP

We study globally supersymmetric 3d gauge theories on curved manifolds by describing the coupling of 3d topological gauge theories, with both Yang-Mills and Chern-Simons terms in the action, to background topological gravity. In our approach the Seifert condition for manifolds supporting global supersymmetry is elegantly deduced from the topological gravity BRST transformations. A cohomological characterization of the geometrical moduli which affect the partition function is obtained. In the Seifert context Chern-Simons topological (framing) anomaly is BRST trivial. We compute explicitly the corresponding local Wess-Zumino functional. As an application, we obtain the dependence on the Seifert moduli of the partition function of 3d supersymmetric gauge theory on the squashed sphere by solving the anomalous topological Ward identities, in a regularization independent way and without the need of evaluating any functional determinant., Comment: 31 pages; v2: some comments added, references added; v3: published version, 1+34 pages, one appendix explaining the relation with the supergravity approach added, minor comments and two references added

Very few AdS_6 x M_4 supersymmetric solutions are known: one in massive IIA, and two IIB solutions dual to it. The IIA solution is known to be unique; in this paper, we use the pure spinor approach to give a classification for IIB supergravity. We reduce the problem to two PDEs on a two-dimensional space Sigma. M_4 is then a fibration of S^2 over Sigma; the metric and fluxes are completely determined in terms of the solution to the PDEs. The results seem likely to accommodate near-horizon limits of (p,q)-fivebrane webs studied in the literature as a source of CFT_5's. We also show that there are no AdS_6 solutions in eleven-dimensional supergravity., Comment: 37 pages; v2: references and equations (5.1) added, version published in Journal of High Energy Physics; v3: equation (5.1b) corrected

We derive the conditions for unbroken supersymmetry for a Mink_2, (2,0) vacuum, arising from Type II supergravity on a compact eight-dimensional manifold M_8. When specialized to internal manifolds enjoying SU(4)xSU(4) structure the resulting system is elegantly rewritten in terms of generalized complex geometry. This particular class of vacua violates the correspondence between supersymmetry conditions and calibrations conditions of D branes (supersymmetry-calibrations correspondence). Our analysis includes and extends previous results about the failure of the supersymmetry-calibrations correspondence, and confirms the existence of a precise relation between such a failure and a subset of the supersymmetry conditions., Comment: 31 pages, 1 figure. v2: minor corrections, references added

In M-theory, the only AdS_7 supersymmetric solutions are AdS_7 x S^4 and its orbifolds. In this paper, we find and classify new supersymmetric solutions of the type AdS_7 x M_3 in type II supergravity. While in IIB none exist, in IIA with Romans mass (which does not lift to M-theory) there are many new ones. We use a pure spinor approach reminiscent of generalized complex geometry. Without the need for any Ansatz, the system determines uniquely the form of the metric and fluxes, up to solving a system of ODEs. Namely, the metric on M_3 is that of an S^2 fibered over an interval; this is consistent with the Sp(1) R-symmetry of the holographically dual (1,0) theory. By including D8 brane sources, one can numerically obtain regular solutions, where topologically M_3 = S^3., Comment: 45 pages, 4 figures. v2: solution with single D8 added; references added; minor corrections

We rewrite the equations for ten-dimensional supersymmetry in a way formally identical to a necessary and sufficient G-structure system in N=2 gauged supergravity, where all four-dimensional quantities are replaced by combinations of pure spinors and fluxes in the internal space. This provides a way to look for lifts of BPS solutions without having to reduce or even rewrite the ten-dimensional action. In particular this avoids the problem of consistent truncation, and the introduction of unphysical gravitino multiplets., Comment: 61 pages

We construct an action for holomorphic Chern-Simons theory that couples the gauge field to off-shell gravitational backgrounds, comprising the complex structure and the (3,0)-form of the target space. Gauge invariance of the off-shell action is achieved by enlarging the field space to include an appropriate system of Lagrange multipliers, ghost and ghost-for-ghost fields. Both the BRST transformations and the BV action are compactly and neatly written in terms of superfields which include fields, backgrounds and their antifields. We show that the anti-holomorphic target space derivative can be written as a BRST-commutator on a functional space containing the anti-fields of both the dynamical fields and the gravitational backgrounds. We derive from this result a Ward identity that determines the anti-holomorphic dependence of physical correlators., Comment: 21 pages