Large Charge Sector of 3d Parity-Violating CFTs

TL;DR

This paper studies the spectrum of large charge operators in 3d parity-violating conformal field theories, revealing a unique parity-violating term in the effective field theory that leads to vortex configurations and richer spectra.

Contribution

It identifies a single quantized parity-violating term in the Goldstone effective field theory for 3d superfluids, affecting the spectrum of large charge operators.

Findings

Presence of a unique parity-violating 1-derivative term in 3d EFT.

Ground state vortices lead to a richer operator spectrum.

Validation in a weakly coupled Chern-Simons matter theory.

Abstract

Certain CFTs with a global $U(1)$ symmetry become superfluids when coupled to a chemical potential. When this happens, a Goldstone effective field theory controls the spectrum and correlators of the lightest large charge operators. We show that in 3d, this EFT contains a single parity-violating 1-derivative term with quantized coefficient. This term forces the superfluid ground state to have vortices on the sphere, leading to a spectrum of large charge operators that is remarkably richer than in parity-invariant CFTs. We test our predictions in a weakly coupled Chern-Simons matter theory.