The algebra of anomaly interplay

TL;DR

This paper provides a mathematical framework using (co)bordism to understand the complex interplay between local and global anomalies across multiple dimensions, enhancing the calculation of global anomalies from local data.

Contribution

It introduces a bordism-based approach to describe and analyze the interplay between local and global anomalies, with examples in 2, 4, and 6 dimensions.

Findings

Mathematical description of anomaly interplay via (co)bordism

Examples of anomaly interplay in multiple dimensions

A rigorous bordism-based method for calculating global anomalies

Abstract

We give a general description of the interplay that can occur between local and global anomalies, in terms of (co)bordism. Mathematically, such an interplay is encoded in the non-canonical splitting of short exact sequences known to classify invertible field theories. We study various examples of the phenomenon in 2, 4, and 6 dimensions. We also describe how this understanding of anomaly interplay provides a rigorous bordism-based version of an old method for calculating global anomalies (starting from local anomalies in a related theory) due to Elitzur and Nair.