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

TL;DR

This paper introduces new $ ext{N}=2$ supersymmetric SYK models with multiple $U(1)$ symmetries and non-zero background charge, revealing novel phases and a phase transition related to black hole physics.

Contribution

It proposes a novel $ ext{N}=2$ SYK model with multiple symmetries and analyzes its low-temperature conformal solutions and phase transitions.

Findings

Emergence of super-Schwarzian mode at low temperatures

Fermion scaling dimension depends on background charge

Identification of a high to low entropy phase transition

Abstract

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.