Phases of $$ \mathcal{N} $$ = 2 Sachdev-Ye-Kitaev models
Matthew Heydeman, Gustavo J. Turiaci, Wen Zhao
Abstract
A bstract We study $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 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 $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 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.