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Nadav Brukner

Bio: Nadav Brukner is an academic researcher from Weizmann Institute of Science. The author has contributed to research in topics: Ansatz & Limit (mathematics). The author has an hindex of 2, co-authored 4 publications receiving 25 citations.

Papers
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TL;DR: In this article, the exact density of states and 2-point function of the SUSY model in the large N double-scaled limit were derived by using combinatorial tools that relate the moments of the distribution to sums over oriented chord diagrams.
Abstract: We compute the exact density of states and 2-point function of the $$ \mathcal{N} $$ = 2 super-symmetric SYK model in the large N double-scaled limit, by using combinatorial tools that relate the moments of the distribution to sums over oriented chord diagrams. In particular we show how SUSY is realized on the (highly degenerate) Hilbert space of chords. We further calculate analytically the number of ground states of the model in each charge sector at finite N, and compare it to the results from the double-scaled limit. Our results reduce to the super-Schwarzian action in the low energy short interaction length limit. They imply that the conformal ansatz of the 2-point function is inconsistent due to the large number of ground states, and we show how to add this contribution. We also discuss the relation of the model to SLq(2|1). For completeness we present an overview of the $$ \mathcal{N} $$ = 1 super-symmetric SYK model in the large N double-scaled limit.

33 citations

Journal ArticleDOI
TL;DR: In this article, the exact density of states and 2-point function of the super-symmetric SYK model in the large $N$ double-scaled limit, by using combinatorial tools that relate the moments of the distribution to sums over oriented chord diagrams, were derived.
Abstract: We compute the exact density of states and 2-point function of the $\mathcal{N} =2$ super-symmetric SYK model in the large $N$ double-scaled limit, by using combinatorial tools that relate the moments of the distribution to sums over oriented chord diagrams. In particular we show how SUSY is realized on the (highly degenerate) Hilbert space of chords. We further calculate analytically the number of ground states of the model in each charge sector at finite $N$, and compare it to the results from the double-scaled limit. Our results reduce to the super-Schwarzian action in the low energy short interaction length limit. They imply that the conformal ansatz of the 2-point function is inconsistent due to the large number of ground states, and we show how to add this contribution. We also discuss the relation of the model to $SL_q(2|1)$. For completeness we present an overview of the $\mathcal{N}=1$ super-symmetric SYK model in the large $N$ double-scaled limit.

13 citations

Journal ArticleDOI
TL;DR: In this article, the role of global fluctuations in the density of states of the SYK model is investigated, showing that the dominant diagrams are given by 1PI cactus graphs and derive a vector model of the couplings which reproduces these results.
Abstract: We consider multi-energy level distributions in the SYK model, and in particular, the role of global fluctuations in the density of states of the SYK model. The connected contributions to the moments of the density of states go to zero as N → ∞, however, they are much larger than the standard RMT correlations. We provide a diagrammatic description of the leading behavior of these connected moments, showing that the dominant diagrams are given by 1PI cactus graphs, and derive a vector model of the couplings which reproduces these results. We generalize these results to the first subleading corrections, and to fluctuations of correlation functions. In either case, the new set of correlations between traces (i.e. between boundaries) are not associated with, and are much larger than, the ones given by topological wormholes. The connected contributions that we discuss are the beginning of an infinite series of terms, associated with more and more information about the ensemble of couplings, which hints towards the dual of a single realization. In particular, we suggest that incorporating them in the gravity description requires the introduction of new, lighter and lighter, fields in the bulk with fluctuating boundary couplings.

8 citations

DOI
TL;DR: It is suggested that a semiclassical wormhole corresponds to a certain class of such density matrices, and how they are constructed is specified, and it is shown that this language allows for a finer criteria for when the wormhole is semiclassicals, which goes beyond entanglement.

7 citations

Posted Content
TL;DR: In this article, the role of global fluctuations in the density of states of the SYK model is investigated, showing that the dominant diagrams are given by 1PI cactus graphs and derive a vector model of couplings which reproduces these results.
Abstract: We consider multi-energy level distributions in the SYK model, and in particular, the role of global fluctuations in the density of states of the SYK model The connected contributions to the moments of the density of states go to zero as $N \to \infty$, however, they are much larger than the standard RMT correlations We provide a diagrammatic description of the leading behavior of these connected moments, showing that the dominant diagrams are given by 1PI cactus graphs, and derive a vector model of the couplings which reproduces these results We generalize these results to the first subleading corrections, and to fluctuations of correlation functions In either case, the new set of correlations between traces (ie between boundaries) are not associated with, and are much larger than, the ones given by topological wormholes The connected contributions that we discuss are the beginning of an infinite series of terms, associated with more and more information about the ensemble of couplings, which hints towards the dual of a single realization In particular, we suggest that incorporating them in the gravity description requires the introduction of new, lighter and lighter, fields in the bulk with fluctuating boundary couplings

Cited by
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Journal ArticleDOI
TL;DR: In this article, Liouville gravity and minimal string theory on spaces with fixed length boundaries were studied, and explicit formulas describing the gravitational dressing of bulk and boundary correlators in the disk were given.
Abstract: We study two-dimensional Liouville gravity and minimal string theory on spaces with fixed length boundaries. We find explicit formulas describing the gravitational dressing of bulk and boundary correlators in the disk. Their structure has a striking resemblance with observables in 2d BF (plus a boundary term), associated to a quantum deformation of SL(2, ℝ), a connection we develop in some detail. For the case of the (2, p) minimal string theory, we compare and match the results from the continuum approach with a matrix model calculation, and verify that in the large p limit the correlators match with Jackiw-Teitelboim gravity. We consider multi-boundary amplitudes that we write in terms of gluing bulk one-point functions using a quantum deformation of the Weil-Petersson volumes and gluing measures. Generating functions for genus zero Weil-Petersson volumes are derived, taking the large p limit. Finally, we present preliminary evidence that the bulk theory can be interpreted as a 2d dilaton gravity model with a sinh Φ dilaton potential.

72 citations

Posted Content
TL;DR: In this article, the mass gap between an extremal black hole and the lightest near-extremal state was shown to exist in the case of near-BPS black holes with an AdS$_2$ throat.
Abstract: 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.

56 citations

Journal ArticleDOI
TL;DR: In this article, Liouville gravity and minimal string theory on spaces with fixed length boundaries were studied, and explicit formulas describing the gravitational dressing of bulk and boundary correlators in the disk were given.
Abstract: We study two-dimensional Liouville gravity and minimal string theory on spaces with fixed length boundaries. We find explicit formulas describing the gravitational dressing of bulk and boundary correlators in the disk. Their structure has a striking resemblance with observables in 2d BF (plus a boundary term), associated to a quantum deformation of $SL(2,\mathbb{R})$, a connection we develop in some detail. For the case of the $(2,p)$ minimal string theory, we compare and match the results from the continuum approach with a matrix model calculation, and verify that in the large $p$ limit the correlators match with Jackiw-Teitelboim gravity. We consider multi-boundary amplitudes that we write in terms of gluing bulk one-point functions using a quantum deformation of the Weil-Petersson volumes and gluing measures. Generating functions for genus zero Weil-Petersson volumes are derived, taking the large $p$ limit. Finally, we present preliminary evidence that the bulk theory can be interpreted as a 2d dilaton gravity model with a $\sinh \Phi$ dilaton potential.

45 citations

Journal ArticleDOI
TL;DR: In this article, the authors derived explicit expressions for a specific subclass of JT gravity bilocal correlators, corresponding to degenerate Virasoro representations, and showed that the series is asymptotic for generic weight h ∉ −ℕ/2.
Abstract: We derive explicit expressions for a specific subclass of Jackiw-Teitelboim (JT) gravity bilocal correlators, corresponding to degenerate Virasoro representations. On the disk, these degenerate correlators are structurally simple, and they allow us to shed light on the 1/C Schwarzian bilocal perturbation series. In particular, we prove that the series is asymptotic for generic weight h ∉ −ℕ/2. Inspired by its minimal string ancestor, we propose an expression for higher genus corrections to the degenerate correlators. We discuss the extension to the $$ \mathcal{N} $$ = 1 super JT model. On the disk, we similarly derive properties of the 1/C super-Schwarzian perturbation series, which we independently develop as well. As a byproduct, it is shown that JT supergravity saturates the chaos bound λL = 2π/β at first order in 1/C. We develop the fixed-length amplitudes of Liouville supergravity at the level of the disk partition function, the bulk one-point function and the boundary two-point functions. In particular we compute the minimal superstring fixed length boundary two-point functions, which limit to the super JT degenerate correlators. We give some comments on higher topology at the end.

30 citations