Anomaly Matching in 6d $\mathcal{N}=(2,0)$ SCFTs from M5 Cobordism

TL;DR

This paper explores the anomalies of 6d $ ext{(2,0)}$ SCFTs with ADE gauge groups using cobordism theory, highlighting the necessity of exotic structures to match IR effective theories and explaining the Hopf-Wess-Zumino term.

Contribution

It introduces the use of exotic bordism structures to fully characterize anomalies in 6d $ ext{(2,0)}$ SCFTs and connects these to IR effective theories and WZW terms.

Findings

Exotic bordism structures are necessary for anomaly matching.

The approach explains the origin of the Hopf-Wess-Zumino term.

Successful anomaly matching for all ADE gauge groups.

Abstract

We investigate the anomalies of 6d $\mathcal{N} = (2, 0)$ superconformal field theories for any ADE gauge group using the modern characterization of anomalies by cobordism. We propose that, in order to account for all features of the anomaly, a bordism theory with exotic tangential structure is needed. We then attempt to match the anomaly in the IR effective theory on the tensor branch with a suitable WZW term. Once again, we show that the exotic bordism structure is necessary to achieve this. Our results suggest a natural explanation for the origin of the Hopf-Wess-Zumino term.