Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Towards a bulk description of higher spin SYK

Hernán A. González, Daniel Grumiller, Jakob Salzer

TL;DR

The paper develops a bulk-to-boundary framework for generalized SYK/JT holography by formulating two-dimensional dilaton gravity as a non-abelian BF theory with SL(2, R) as a gravity subsector and extending it with Yang–Mills and higher-spin symmetries. It derives generalized Schwarzian boundary actions via two routes: (i) an on-shell action with boundary terms respecting symmetries, and (ii) a Lee–Wald–Zoupas-inspired symplectic analysis that yields group-manifold boundary actions and higher-spin Schwarzian analogues. The work provides a unified description of entropy and one-loop corrections in these extended theories, showing that spin-2 dominates at very low temperatures while higher spins contribute through Casimir-related terms and logarithmic corrections, and it builds a holographic dictionary linking bulk data to SYK-like couplings and temperature. These results broaden the landscape of SYK-like holography, offering a structured route to incorporate Yang–Mills and higher-spin dynamics into the low-energy, Schwarzian-dominated regime and setting the stage for further explorations of W-algebras in two-dimensional holography.

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.

Towards a bulk description of higher spin SYK

TL;DR

The paper develops a bulk-to-boundary framework for generalized SYK/JT holography by formulating two-dimensional dilaton gravity as a non-abelian BF theory with SL(2, R) as a gravity subsector and extending it with Yang–Mills and higher-spin symmetries. It derives generalized Schwarzian boundary actions via two routes: (i) an on-shell action with boundary terms respecting symmetries, and (ii) a Lee–Wald–Zoupas-inspired symplectic analysis that yields group-manifold boundary actions and higher-spin Schwarzian analogues. The work provides a unified description of entropy and one-loop corrections in these extended theories, showing that spin-2 dominates at very low temperatures while higher spins contribute through Casimir-related terms and logarithmic corrections, and it builds a holographic dictionary linking bulk data to SYK-like couplings and temperature. These results broaden the landscape of SYK-like holography, offering a structured route to incorporate Yang–Mills and higher-spin dynamics into the low-energy, Schwarzian-dominated regime and setting the stage for further explorations of W-algebras in two-dimensional holography.

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.

Paper Structure

This paper contains 27 sections, 146 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. Dilaton gravity as generalized BF-theory
  3. Bulk action and equations of motion
  4. Observables
  5. Action principle
  6. Jackiw--Teitelboim model
  7. Boundary and integrability conditions
  8. Action principle and on-shell action
  9. Boundary action from Casimir
  10. Yang--Mills extensions of SYK
  11. Boundary conditions
  12. Boundary action
  13. Interpretation as dilaton gravity-Yang--Mills theory
  14. Towards higher spin SYK
  15. Spin-3 boundary conditions
  16. ...and 12 more sections

Figures (1)

  • Figure 1: Finite temperature and asymptotic symmetry in the gauge theory formulation. Euclidean black holes are represented by fields $(\mathcal{A},\mathcal{X})$ in a cigar-type geometry. The "Euclidean horizon" is located at $\rho=0$. Demanding the black hole to be at Hawking temperature (absence of holonomies, ${\rm H}[\mathcal{A}]=\pm1\space\text{l}$) affects the asymptotic symmetries. The asymptotic fields $(\mathcal{A}_{\infty}(\tau),\mathcal{X}_{\infty}(\tau))$ become $(\mathcal{A}_G(\tau),\mathcal{X}_G(\tau))$ consistently with smoothness of the solutions.