Compensating strong coupling with large charge

TL;DR

This paper explores the behavior of conformal field theories with global symmetries at large charge, revealing that large charge induces weak coupling and describing low-energy excitations via Goldstone's theorem.

Contribution

It demonstrates that large global charge results in effective couplings decreasing with charge, and provides a framework for computing anomalous dimensions in this regime.

Findings

Large charge leads to weak effective couplings.

Goldstone modes describe low-energy excitations at large charge.

Outline for calculating anomalous dimensions in the large charge limit.

Abstract

We study some (conformal) field theories with global symmetries in the sector where the value of the global charge $Q$ is large. We find (as expected) that the low energy excitations of this sector are described by the general form of Goldstone's theorem in the non-relativistic regime. We also derive the unexpected result, first presented in [Hellerman et al. 2015], that the effective field theory describing such sector of fixed $Q$ contains effective couplings $\lambda_{\text{eff}}\sim \lambda^b /Q^{a}$, where $\lambda$ is the original coupling. Hence, large charge leads to weak coupling. In the last section of the paper we present an outline of how to compute anomalous dimensions of the $O(n)$ model in this limit.