Bi-Local Holography in the SYK Model: Perturbations

TL;DR

This work develops a reparametrization-invariant bi-local collective field framework for the large-N SYK model and performs perturbative expansions around the IR conformal point, incorporating zero-mode dynamics via a Schwarzian action. It computes the shift of the classical background (Psi0 → Psi0+Psi1+Psi2) and extends to all orders in q>2 with a recursion for higher-order coefficients, while also analyzing the bi-local two-point function. At finite temperature, the authors obtain finite-T classical solutions and derive the tree-level free energy as a systematic beta J expansion, matching known numerical results and reinforcing the connection to AdS2 holography. The methodology provides a controlled, gauge-fixed route to include Schwarzian and bi-local interactions in a unified perturbative scheme with potential loop corrections and holographic implications.

Abstract

We continue the study of the Sachdev-Ye-Kitaev model in the Large $N$ limit. Following our formulation in terms of bi-local collective fields with dynamical reparametrization symmetry, we perform perturbative calculations around the conformal IR point.

Figures (1)

• Figure 1: $f_0(y)$ and $F_0(y, q)$ with $q=2, 4, 1000$ in the range of $-\frac{1}{2} \le y \le \frac{1}{2}$.