A Scaling Limit for Line and Surface Defects

TL;DR

This paper introduces a new scaling limit inspired by large charge expansion to analyze defect conformal field theories in various dimensions, providing beta functions and correlation functions for defects with symmetry-breaking and symmetry-preserving properties.

Contribution

It develops a novel scaling limit approach to study defect CFTs, enabling the calculation of beta functions and correlation functions for defects in theories with different global symmetries.

Findings

Computed the beta function for defect coupling.

Derived correlation functions of defect operators with large charge.

Identified defect conformal field theories in the studied models.

Abstract

We study symmetry-breaking line defects in the Wilson-Fisher theory with $O(2N+1)$ global symmetry near four dimensions and symmetry-preserving surface defects in a cubic model with $O(2N)$ global symmetry near six dimensions. We introduce a scaling limit inspired by the large charge expansion in Conformal Field Theory. Using this, we compute the beta function for the defect coupling which allows to identify the corresponding Defect Conformal Field Theories. We also compute the correlation function of two parallel defects as well as correlation functions of certain defect operators with large charge under the surviving symmetry.