Charging the Walking U(N)$\times$U(N) Higgs Theory as a Complex CFT

TL;DR

This paper uses a semi-classical approach to compute conformal data for a complex fixed point in a non-abelian Higgs theory, validating the method against perturbative results.

Contribution

It introduces a semi-classical method to analyze a complex CFT in a multi-coupling non-abelian Higgs theory, providing new insights into its operator dimensions.

Findings

Computed scaling dimensions match perturbative results

Validated the semi-classical approach for complex CFTs

Identified operator families in the U(N)xU(N) Higgs theory

Abstract

We apply a semi-classical method to compute the conformal field theory (CFT) data for the U(N)xU(N) non-abelian Higgs theory in four minus epsilon dimensions at its complex fixed point. The theory features more than one coupling and walking dynamics. Given our charge configuration, we identify a family of corresponding operators and compute their scaling dimensions which remarkably agree with available results from conventional perturbation theory validating the use of the state-operator correspondence for a complex CFT.