The $\epsilon$-expansion of the codimension two twist defect from conformal field theory

TL;DR

This paper computes the scaling dimensions of operators on a codimension two twist defect at the Wilson-Fisher fixed point using the epsilon-expansion, avoiding Feynman diagrams and confirming known results.

Contribution

It applies the Rychkov-Tan framework to the twist defect in 4-epsilon dimensions, providing a novel epsilon-expansion calculation without Feynman diagrams.

Findings

Scaling dimensions obtained up to first nontrivial order in epsilon

Results agree with previously known data

Method offers a diagram-free approach to defect CFT analysis

Abstract

We apply the framework of Rychkov-Tan arXiv:1505.00963 to the codimension two twist defect at the Wilson-Fisher fixed point in $4-\epsilon$ dimensions. We obtain the scaling dimensions of the operators on the defect up to the lowest nontrivial order in the $\epsilon$-expansion without using Feynman diagram computation. Our results agree with the known results.