A supersymmetric SYK model with a curious low energy behavior

TL;DR

This paper investigates supersymmetric SYK models with unusual low energy entropy behavior, revealing that their low energy physics is dominated by scalar field fluctuations without evidence of a spin glass phase.

Contribution

It reanalyzes the large N equations of supersymmetric SYK models to clarify their low energy behavior and rules out the existence of a spin glass phase.

Findings

Scalar fields develop large expectation values exploring low energy valleys.

Low energy physics is dominated by quadratic fluctuations.

No evidence of a spin glass phase was found.

Abstract

We consider $\mathcal{N}$ = 2, 4 supersymmetric SYK models that have a peculiar low energy behavior, with the entropy going like $S = S_{0} + \text{(constant)}T^{a}$, where $a \neq 1$. The large $N$ equations for these models are a generalization of equations that have been previously studied as an unjustified truncation of the planar diagrams describing the BFSS matrix quantum mechanics or other related matrix models. Here we reanalyze these equations in order to better understand the low energy physics of these models. We find that the scalar fields develop large expectation values which explore the low energy valleys in the potential. The low energy physics is dominated by quadratic fluctuations around these values. These models were previously conjectured to have a spin glass phase. We did not find any evidence for this phase by using the usual diagnostics, such as searching for replica symmetry breaking solutions.