Towards a bulk description of higher spin SYK

TL;DR

This paper extends the SYK model holographically to include higher spins and Yang--Mills fields by generalizing the JT model and deriving a generalized Schwarzian action, exploring entropy corrections and holographic dualities.

Contribution

It introduces a framework for higher spin and Yang--Mills extensions of the SYK/JT correspondence using BF formulation and boundary term analysis.

Findings

Generalized Schwarzian action derived for higher spin extensions.

Analysis of entropy including higher spin log-corrections.

Holographic dictionary established for the extended SYK/JT models.

Abstract

We consider on the bulk side extensions of the Sachdev--Ye--Kitaev (SYK) model to Yang--Mills and higher spins. To this end we study generalizations of the Jackiw--Teitelboim (JT) model in the BF formulation. Our main goal is to obtain generalizations of the Schwarzian action, which we achieve in two ways: by considering the on-shell action supplemented by suitable boundary terms compatible with all symmetries, and by applying the Lee--Wald--Zoupas formalism to analyze the symplectic structure of dilaton gravity. We conclude with a discussion of the entropy (including log-corrections from higher spins) and a holographic dictionary for the generalized SYK/JT correspondence.