$\epsilon$-Expansion in the Gross-Neveu CFT

TL;DR

This paper applies conformal field theory techniques to compute anomalous dimensions in the Gross-Neveu model near two dimensions, extending existing algorithms to fermionic theories and confirming results with Feynman diagrams.

Contribution

It extends the cowpie contraction algorithm to fermionic theories and demonstrates the effectiveness of CFT techniques in calculating anomalous dimensions in the Gross-Neveu model.

Findings

Results match Feynman diagram computations

Extended cowpie contraction algorithm for fermions

Validated CFT approach for fermionic models

Abstract

We use the recently developed CFT techniques of Rychkov and Tan to compute anomalous dimensions in the $O(N)$ Gross-Neveu model in $d=2+\epsilon$ dimensions. To do this, we extend the "cowpie contraction" algorithm of arXiv:1506.06616 to theories with fermions. Our results match perfectly with Feynman diagram computations.