Phases of $$ \mathcal{N} $$ = 2 Sachdev-Ye-Kitaev models

Abstract

We study $$ \mathcal{N} $$ N = 2 supersymmetric Sachdev-Ye-Kitaev (SYK) models with com- plex fermions at non-zero background charge. Motivated by multi-charge supersymmetric black holes, we propose a new $$ \mathcal{N} $$ 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 AdS2/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.

A quantum mechanics for magnetic horizons

“…It would be consistent to neglect those terms if Ξ 1, which is classically dimensionless, gained a positive anomalous dimension. This is indeed the case for classically dimensionless fermions in SYK models such as [31,32], but it remains to be checked in the theory discussed here.…”

“…Therefore, although the quantum mechanics is specific and well defined, we expect that at large N its couplings could be approximated by random variables following a suitable statistical distribution. This makes us hopeful that the IR dynamics might have some traits in common with supersymmetric SYK models [31,32]. The idea of obtaining a supersymmetric QM with fixed, but statistically distributed, couplings that could describe near-extremal horizons already appeared in [33] in the context of asymptotically-flat black holes in string theory.…”

Solvable models of quantum black holes: a review on Jackiw–Teitelboim gravity

“…( 2022 ) and Heydeman et al. ( 2023 ). The time-ordered correlators were computed recently in Lin et al.…”

“…The disk partition function was computed in Stanford and Witten (2017), and the density of states in Mertens et al (2017). This theory can have fractional charge and also be supplemented by a theta angle, see Boruch et al (2022) and Heydeman et al (2023). The time-ordered correlators were computed recently in Lin et al (2023a, b).…”

A string-theoretical analog of non-maximal chaos in some Sachdev-Ye-Kitaev-like models

“…This correspondence does not exist in canonical nonlinear dynamics, and builds up a deep connection between novel chaotic phenomena and black hole physics. On the other hand, the SYK model allows nice embedding of various SUSY(-like) structures, whose consequences are currently under investigations [1,20,21,[42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58]. So it is natural to ask whether and how these structures influence system's chaotic behaviors.…”