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High Energy Physics - Theory
Title: $\mathcal{N}=2$ SYK models with dynamical bosons and fermions
(Submitted on 13 Feb 2024 (v1), last revised 18 Apr 2024 (this version, v2))
Abstract: We study a class of SYK models with $\mathcal{N}=2$ supersymmetry, described by $N$ fermions in chiral Fermi multiplets, as well as $\alpha N$ first-order bosons in chiral multiplets. The interactions are characterised by two integers $(p,q)$. We focus on the large $N$ and low energy limit of these models. Despite the presence of dynamical bosons, we find conformal behaviour akin to the standard SYK model. We use $\mathcal{I}$-extremization of a Witten index to study the supersymmetric solutions. In particular, we find an exact expression for the entropy, which matches the numerical solutions to the Schwinger-Dyson equations. We further solve the model both in the large $p$ and large $p,q$ limits. Numerically, we verify our analytical results and obtain estimates for the Schwarzian coupling in the near zero-temperature limit. We also study the low-lying spectrum of operators to determine the parameter ranges where the Schwarzian mode dominates the IR dynamics. Lastly, we study out-of-time-ordered correlators to show that the model is maximally chaotic.
Submission history
From: Francesco Benini [view email][v1] Tue, 13 Feb 2024 12:37:41 GMT (849kb,D)
[v2] Thu, 18 Apr 2024 11:30:39 GMT (848kb,D)
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