Four-point function of the complex Sachdev-Ye-Kitaev model at finite chemical potential

TL;DR

This paper computes the four-point function of the complex Sachdev-Ye-Kitaev model at finite chemical potential, revealing its conformal structure and extracting key correlation constants in the infrared regime.

Contribution

It provides the first explicit calculation of the four-point function at arbitrary asymmetry parameter, confirming the NCFT$_{1}$ structure of the cSYK model.

Findings

Four-point function consistent with NCFT$_{1}$ structure

Explicit structure constants for fermion bilinear correlators

Validation of conformal limit behavior at finite chemical potential

Abstract

It is known that, for a range of chemical potentials, the infrared behavior of the complex Sachdev-Ye-Kitaev (cSYK) model is governed by a 1D Nearly Conformal Field Theory (NCFT$_{1}$), thereby realizing a continuous line of NCFTs. A finite chemical potential $\mu$ introduces an asymmetry parameter $\mathscr{E}$ into the cSYK fermion two-point function in the conformal limit. In this work, we compute the cSYK four-point function in the conformal limit for an arbitrary value of $\mathscr{E}$ at leading order in $1/N$. We show that the result is fully consistent with the NCFT$_{1}$ structure of the cSYK model and use it to extract the structure constants for correlation functions of two complex fermions with bilinear operators.