Line Defect RG Flows in the $\varepsilon$ Expansion

TL;DR

This paper analyzes line defect RG flows in scalar and scalar-fermion theories below four dimensions using the $ ext{epsilon}$ expansion, computing defect beta functions and exploring IR stable defect conformal field theories.

Contribution

It provides the first next-to-leading order calculation of defect beta functions for general scalar-fermion theories and discusses multiple IR stable defect CFTs with specific symmetries.

Findings

Computed defect beta functions to next-to-leading order.

Identified conditions for multiple IR stable defect CFTs.

Calculated one-point function coefficients in specific models.

Abstract

A general analysis of line defect renormalisation group (RG) flows in the $\varepsilon$ expansion below $d=4$ dimensions is undertaken. The defect beta function for general scalar-fermion bulk theories is computed to next-to-leading order in the bulk couplings. Scalar models as well as scalar-fermion models with various global symmetries in the bulk are considered at leading non-trivial order. Different types of potential infrared (IR) defect conformal field theories (dCFTs) and their RG stability are discussed. The possibility of multiple IR stable dCFTs is realised in specific examples with hypertetrahedral symmetry in the bulk. The one-point function coefficient of the order parameter in the stable IR dCFT of the cubic model is computed at next-to-leading order and compared with that in the IR dCFT of the Heisenberg model.