Scaling limits of complex Sachdev-Ye-Kitaev models and holographic geometry

TL;DR

This paper analyzes various scaling limits of the complex Sachdev-Ye-Kitaev model, computes key physical quantities, and connects these results to holographic duality with Jackiw-Teitelboim gravity including a gauge field.

Contribution

It introduces a comprehensive analysis of large $N$ and $p$ limits, including a double-scaling limit, and establishes a holographic correspondence with JT gravity with a $U(1)$ gauge field.

Findings

Matching results between different large $N,p$ limits.

Resummation of small $rac{ ext{p}^2}{N}$ expansions.

Holographic duality with 2D Jackiw-Teitelboim gravity with gauge field.

Abstract

We compare different limits of the Sachdev-Ye-Kitaev model of $N$ complex fermion with $p$-fermion interactions. First, we compute the fermion Green's function and free energy in the limit of large $N$ followed subsequently by the limit of large $p$. Next, we examine the `double-scaling' limit in which the large $N,p$ limits are taken at fixed $\lambda = p^2/N$. Earlier results on the latter limit are resummed for small $\lambda$, and shown to match our results for the first limit. We also describe the holographic match of our results to two-dimensional Jackiw-Teitelboim gravity with an additional $U(1)$ gauge field.