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arXiv · 2206.14900

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

Matthew Heydeman·Gustavo J. Turiaci·Wenli Zhao
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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.

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Matthew Heydeman, Gustavo J. Turiaci, Wenli Zhao. 2022-10-27. Phases of $\mathcal{N}=2$ Sachdev-Ye-Kitaev models. https://doi.org/10.1007/jhep01(2023)098

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