Charging the conformal window at nonzero $\theta$ angle

TL;DR

This paper explores how the $ heta$-angle and axion physics influence the near conformal dynamics of large-charge baryon sectors in $SU(2)$ gauge theories, using an effective field theory approach with Goldstone and dilaton fields.

Contribution

It introduces a systematic effective framework incorporating topological terms to analyze the impact of $ heta$-angle and dilaton potentials on conformal dimensions.

Findings

Computed corrections to conformal dimensions as functions of $ heta$ and dilaton potentials.

Analyzed effects of different dilaton potentials on conformal dynamics.

Provided insights into topological effects in near conformal gauge theories.

Abstract

We determine the impact of the $\theta$-angle and axion physics on the near conformal dynamics of the large-charge baryon sector of $SU(2)$ gauge theories with $N_f$ fermions in the fundamental representation. We employ an effective approach featuring Goldstone and dilaton degrees of freedom augmented by the topological terms in the theory. We investigate how different dilaton potentials, including the ones for which a systematic counting scheme can be established, affect the results. Via state-operator correspondence we compute the corrections to the would-be conformal dimensions of the lowest large-charge operators as a function of the $\theta$ term and dilaton potential.