Anomalies for Galilean fields

TL;DR

This paper systematically studies 't Hooft anomalies in Galilean field theories, revealing how relativistic anomalies translate under DLCQ and classifying Weyl anomalies in Schrödinger CFTs, with implications for dual string theories.

Contribution

It classifies pure Weyl anomalies in Schrödinger theories and analyzes the persistence of relativistic anomalies under DLCQ, advancing understanding of non-relativistic field theory anomalies.

Findings

Anomalies survive DLCQ as mixed anomalies.

No pure Weyl anomalies in even dimensions.

Lowest-derivative anomalies in odd dimensions relate to higher-dimensional relativistic CFTs.

Abstract

We initiate a systematic study of `t Hooft anomalies in Galilean field theories, focusing on two questions therein. In the first, we consider the non-relativistic theories obtained from a discrete light-cone quantization (DLCQ) of a relativistic theory with flavor or gravitational anomalies. We find that these anomalies survive the DLCQ, becoming mixed flavor/boost or gravitational/boost anomalies. We also classify the pure Weyl anomalies of Schr\"odinger theories, which are Galilean conformal field theories (CFTs) with $z=2$. There are no pure Weyl anomalies in even spacetime dimension, and the lowest-derivative anomalies in odd dimension are in one-to-one correspondence with those of a relativistic CFT in one dimension higher. These results classify many of the anomalies that arise in the field theories dual to string theory on Schr\"odinger spacetimes.