The epsilon expansion of the O$(N)$ model with line defect from conformal field theory

TL;DR

This paper uses conformal field theory axioms to analyze the critical O(N) model with a line defect in (4−ε) dimensions, determining defect couplings and operator dimensions without diagrammatic methods.

Contribution

It introduces an axiomatic approach to compute defect operator dimensions and fixed point couplings in the O(N) model, avoiding traditional perturbative calculations.

Findings

Fixed point defect coupling is uniquely determined by axioms.

Leading anomalous dimensions match perturbative results.

Analyticity of correlators is crucial for operator dimension calculations.

Abstract

We employ the axiomatic framework of Rychkov and Tan to investigate the critical O$(N)$ vector model with a line defect in $(4-\epsilon)$ dimensions. We assume the fixed point is described by defect conformal field theory and show that the critical value of the defect coupling to the bulk field is uniquely fixed without resorting to diagrammatic calculations. We also study various defect localized operators by the axiomatic method, where the analyticity of correlation functions plays a crucial role in determining the conformal dimensions of defect composite operators. In all cases, including operators with operator mixing, we reproduce the leading anomalous dimensions obtained by perturbative calculations.