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We study $\mathcal{N}=2$ supersymmetric Sachdev-Ye-Kitaev (SYK) models with complex fermions at non-zero background charge. Motivated by multi-charge supersymmetric black holes, we propose a new $\mathcal{N}=2$ SYK model with multiple $U(1)$ symmetries, integer charges, and a non-vanishing supersymmetric index, realizing features not present in known SYK models. In both models, a conformal solution with a super-Schwarzian mode emerges at low temperatures, signalling the appearance of nearly AdS$_2$/BPS physics. However, in contrast to complex SYK, the fermion scaling dimension depends on the background charge in the conformal limit. For a critical charge, we find a high to low entropy phase transition in which the conformal solution ceases to be valid. This transition has a simple interpretation: the fermion scaling dimension violates the unitarity bound. We offer some comments on a holographic interpretation for supersymmetric black holes., Comment: 56+8 pages, 16 figures

We consider $\mathcal{N}=(2,2)$ AdS$_3$/CFT$_2$ dualities proposed in the large central charge limit ($c\to\infty$) by Eberhardt. Here we propose the associated D1-D5 systems to be orbifolds of the standard $\mathcal{N}=(4,4)$ systems, thereby elevating the dualities to the finite-$c$ level on the boundary and to the quantum level in the bulk. In particular, we show that our brane systems yield low-energy sigma models whose subleading central charges match earlier predictions from bulk one-loop supergravity computations. In the case involving the Enriques surface, the finite-$c$ sigma model has a non-trivial elliptic genus which we use to microscopically explain both the Bekenstein-Hawking entropy and the subleading logarithmic correction to it for the associated macroscopic black brane., Comment: 34 pages. v3: minor improvements

Due to the failure of thermodynamics for low temperature near-extremal black holes, it has long been conjectured that a "thermodynamic mass gap" exists between an extremal black hole and the lightest near-extremal state. For non-supersymmetric near-extremal black holes in Einstein gravity, with an AdS$_2$ throat, no such gap was found. Rather, at that energy scale, the spectrum exhibits a continuum of states, up to non-perturbative corrections. In this paper, we compute the partition function of near-BPS black holes in supergravity where the emergent, broken, symmetry is $PSU(1,1|2)$. To reliably compute this partition function, we show that the gravitational path integral can be reduced to that of a $\mathcal N=4$ supersymmetric extension of the Schwarzian theory, which we define and exactly quantize. In contrast to the non-supersymmetric case, we find that black holes in supergravity have a mass gap and a large extremal black hole degeneracy consistent with the Bekenstein-Hawking area. Our results verify several string theory conjectures, concerning the scale of the mass gap and the counting of extremal micro-states., Comment: 82 pages, 5 figures, V2: fixed several typos and added relevant references

As shown in [1], two copies of the large $N$ Majorana SYK model can produce spontaneous breaking of a $Z_2$ symmetry when they are coupled by appropriate quartic terms. In this paper we similarly study two copies of the complex SYK model coupled by a quartic term preserving the $U(1) \times U(1)$ symmetry. We also present a tensor counterpart of this coupled model. When the coefficient $\alpha$ of the quartic term lies in a certain range, the coupled large $N$ theory is nearly conformal. We calculate the scaling dimensions of fermion bilinear operators as functions of $\alpha$. We show that the operator $c_{1i}^\dagger c_{2i}$, which is charged under the axial $U(1)$ symmetry, acquires a complex dimension outside of the line of fixed points. We derive the large $N$ Dyson-Schwinger equations and show that, outside the fixed line, this $U(1)$ symmetry is spontaneously broken at low temperatures because this operator acquires an expectation value. We support these findings by exact diagonalizations extrapolated to large $N$., Comment: 36 pages, 16 figures; v2: some improvements; v3: version to appear in JHEP

We study a large $N$ tensor model with $O(N)^3$ symmetry containing two flavors of Majorana fermions, $\psi_1^{abc}$ and $\psi_2^{abc}$. We also study its random counterpart consisting of two coupled Sachdev-Ye-Kitaev models, each one containing $N_{\rm SYK}$ Majorana fermions. In these models we assume tetrahedral quartic Hamiltonians which depend on a real coupling parameter $\alpha$. We find a duality relation between two Hamiltonians with different values of $\alpha$, which allows us to restrict the model to the range of $-1\leq \alpha\leq 1/3$. The scaling dimension of the fermion number operator $Q=i\psi_1^{abc} \psi_2^{abc}$ is complex and of the form $1/2 +i f(\alpha)$ in the range $-1\leq \alpha<0$, indicating an instability of the conformal phase. Using Schwinger-Dyson equations to solve for the Green functions, we show that in the true low-temperature phase this operator acquires an expectation value. This demonstrates the breaking of an anti-unitary particle-hole symmetry and other discrete symmetries. We also calculate spectra of the coupled SYK models for values of $N_{\rm SYK}$ where exact diagonalizations are possible. For negative $\alpha$ we find a gap separating the two lowest energy states from the rest of the spectrum; this leads to exponential decay of the zero-temperature correlation functions. For $N_{\rm SYK}$ divisible by $4$, the two lowest states have a small splitting. They become degenerate in the large $N_{\rm SYK}$ limit, as expected from the spontaneous breaking of a $\mathbb{Z}_2$ symmetry., Comment: 37 pages, v2: some improvements, references added. v3: added a discussion of separation of spectra into sectors and an Appendix on zero-energy states. The version to appear in Physical Review X

Within eleven dimensional supergravity we compute the logarithmic correction to the entropy of magnetically charged asymptotically AdS${}_4$ black holes with arbitrary horizon topology. We find perfect agreement with the expected microscopic result arising from the dual field theory computation of the topologically twisted index. Our result relies crucially on a particular limit to the extremal black hole case and clarifies some aspects of quantum corrections in asymptotically AdS spacetimes., Comment: 5 pages. V2: Presentation changed, PRL version

The topologically twisted index for ABJM theory with gauge group $U(N)_k \times U(N)_{-k}$ has recently been shown, in the large-$N$ limit, to reproduce the Bekenstein-Hawking entropy of certain magnetically charged asymptotically AdS$_4$ black holes. We numerically study the index beyond the large-$N$ limit and provide evidence that it contains a subleading logarithmic term of the form $-1/2\log N$. On the holographic side, this term naturally arises from a one-loop computation. However, we find that the contribution coming from the near horizon states does not reproduce the field theory answer. We give some possible reasons for this apparent discrepancy., Comment: 17 pages, 2 figures, discussion improved

The large-$N$ limit of ABJM theory is holographically dual to M-theory on AdS$_4\times S^7/\mathbb{Z}_k$. The 3-sphere partition function has been obtained via localization, and its leading behavior $F_{\text{ABJM}}^{(0)}\sim k^{1/2}N^{3/2}$ is exactly reproduced in the dual theory by tree-level supergravity. We extend this comparison to the sub-leading $\mathcal O(N^0)$ order by computing the one-loop supergravity free energy as a function of $k$ and comparing it with the ABJM result. Curiously, we find that the expressions do not match, with $F_{\text{SUGRA}}^{(1)}\sim k^6$, while $F_{\text{ABJM}}^{(1)}\sim k^2$. This suggests that the low-energy approximation $Z_{\text{M-theory}}=Z_{\text{SUGRA}}$ breaks down at one-loop order., Comment: 22 pages, 1 figure, discussion on the O(N^{1/2}) order and references added