Global Anomalies and Effective Field Theory

TL;DR

This paper demonstrates how global anomalies influence effective field theories, explaining the origin of certain couplings and providing measurable predictions like the chiral vortical effect coefficient.

Contribution

It establishes a connection between global anomalies and the structure of effective field theories, especially in thermal contexts, and introduces a new method for calculating global anomalies.

Findings

Global anomalies determine the non-renormalization of certain couplings.

A mixed global anomaly in four dimensions fixes the chiral vortical effect coefficient.

A new correlation function-based method simplifies anomaly calculations.

Abstract

We show that matching anomalies under large gauge transformations and large diffeomorphisms can explain the appearance and non-renormalization of couplings in effective field theory. We focus on thermal effective field theory where we argue that the appearance of certain unusual Chern-Simons couplings is a consequence of global anomalies. As an example, we show that a mixed global anomaly in four dimensions fixes the chiral vortical effect coefficient. This is an experimentally measurable prediction from a global anomaly. For certain situations, we propose a simpler method for calculating global anomalies which uses correlation functions rather than eta invariants.