Global anomalies on Lorentzian space-times

TL;DR

This paper develops an algebraic criterion to detect global anomalies in Lorentzian space-times within locally covariant field theory, successfully reproducing known anomalies like the SU(2) anomaly in four dimensions.

Contribution

It introduces a new algebraic criterion for global anomalies applicable to Lorentzian space-times, extending the theoretical framework of locally covariant field theory.

Findings

Reproduces the known SU(2) anomaly in four dimensions

Provides a general algebraic criterion for global anomalies

Discusses implications for globally hyperbolic space-times

Abstract

We formulate an algebraic criterion for the presence of global anomalies on globally hyperbolic space-times in the framework of locally covariant field theory. We discuss some consequences and check that it reproduces the well-known global $SU(2)$ anomaly in four space-time dimensions.