The background field method and critical vector models

TL;DR

This paper employs the background field method to compute conformal field theory data for critical vector models, including $ ext{phi}^6$ and Gross-Neveu models, providing detailed operator dimensions and OPE coefficients.

Contribution

It systematically derives CFT data for these models using the background field method, extending calculations to next-to-leading order in the $1/N$ expansion.

Findings

Calculated OPE coefficients for critical vector models.

Determined anomalous dimensions of operators in these models.

Extended results to next-to-leading order in $1/N$ expansion.

Abstract

We use the background field method to systematically derive CFT data for the critical $\phi^6$ vector model in three dimensions, and the Gross-Neveu model in dimensions $2\leq d \leq 4$. Specifically, we calculate the OPE coefficients and anomalous dimensions of various operators, up to next-to-leading order in the $1/N$ expansion.