Anomalies, instantons and chiral symmetry breaking at a Lifshitz point

TL;DR

This paper explores chiral anomalies and symmetry breaking in non-relativistic Lifshitz theories, extending classical quantum field theory concepts to new gravitational models with explicit examples and index computations.

Contribution

It introduces a novel analysis of chiral anomalies within Lifshitz theories, emphasizing differences from traditional relativistic models and providing explicit gravitational examples.

Findings

Explicit index computations for Lifshitz models

Differences identified between Lifshitz and ordinary gravity

Extension of chiral anomaly analysis to non-relativistic theories

Abstract

We give a new twist to an old-fashioned topic in quantum field theory describing violations of the chiral charge conservation of massless fermions through Adler-Bell-Jackiw anomalies in the background of instanton fields in the context of non-relativistic Lifshitz theories. The results we report here summarize in a nut-shell our earlier work on the subject found in arXiv:1103.5693 and arXiv:1110.1332. We present simple examples where index computations can be carried out explicitly focusing, in particular, to gravitational models of Lifshitz type and highlight their differences from ordinary gravity in four space-time dimensions.