Nonrelativistic Conformal Field Theories in the Large Charge Sector

TL;DR

This paper develops an effective field theory for nonrelativistic conformal field theories at large charge, revealing universal behaviors and calculating operator dimensions and correlation functions, with potential applications to fermionic and anyonic systems.

Contribution

It constructs a semi-classical EFT for Schrödinger invariant theories in the large charge limit, providing new insights into operator dimensions and correlation functions.

Findings

Universal behavior of three-point functions at large charge

Calculated dimensions of lowest lying operators

Potential relevance to fermions at unitarity and anyon systems

Abstract

We study Schr\"odinger invariant field theories (nonrelativistic conformal field theories) in the large charge (particle number) sector. We do so by constructing the effective field theory (EFT) for a Goldstone boson of the associated $U(1)$ symmetry in a harmonic potential. This EFT can be studied semi-classically in a large charge expansion. We calculate the dimensions of the lowest lying operators, as well as correlation functions of charged operators. We find universal behavior of three point function in large charge sector. We comment on potential applications to fermions at unitarity and critical anyon systems.