Weyl Consistency Conditions in Non-Relativistic Quantum Field Theory

TL;DR

This paper classifies Weyl anomalies and their ambiguities in non-relativistic 2+1 dimensional quantum field theories with z=2 scaling, deriving consistency conditions and exploring potential C-theorems.

Contribution

It extends Weyl anomaly classification and consistency conditions to non-relativistic theories, proposing candidates for a C-theorem in this context.

Findings

Classified Weyl anomalies and scheme ambiguities in 2+1D non-relativistic theories

Derived consistency conditions among anomalies

Identified potential C-theorem candidates

Abstract

Weyl consistency conditions have been used in unitary relativistic quantum field theory to impose constraints on the renormalization group flow of certain quantities. We classify the Weyl anomalies and their renormalization scheme ambiguities for generic non-relativistic theories in 2+1 dimensions with anisotropic scaling exponent z=2; the extension to other values of z are discussed as well. We give the consistency conditions among these anomalies. As an application we find several candidates for a C-theorem. We comment on possible candidates for a $C$-theorem in higher dimensions.