Discrete and higher-form symmetries in SCFTs from wrapped M5-branes

TL;DR

This paper explores how topological BF mass terms in M-theory compactifications lead to various discrete and higher-form symmetries in dual 4d SCFTs, analyzing their anomalies and boundary conditions.

Contribution

It provides a detailed analysis of the global symmetries and 't Hooft anomalies in 4d $ ext{SCFTs}$ from wrapped M5-branes, including the role of boundary conditions and anomaly inflow.

Findings

Identifies different global discrete symmetries from boundary conditions of BF terms.

Computes anomaly polynomial including background fields for various symmetries.

Clarifies the role of axionic backgrounds in anomalies related to coupling constants.

Abstract

We analyze topological mass terms of BF type arising in supersymmetric M-theory compactifications to $AdS_5$. These describe spontaneously broken higher-form gauge symmetries in the bulk. Different choices of boundary conditions for the BF terms yield dual field theories with distinct global discrete symmetries. We discuss in detail these symmetries and their 't Hooft anomalies for 4d $\mathcal N = 1$ SCFTs arising from M5-branes wrapped on a Riemann surface without punctures, including theories from M5-branes at a $\mathbb Z_2$ orbifold singularity. The anomaly polynomial is computed via inflow and contains background fields for discrete global 0-, 1-, and 2-form symmetries and continuous 0-form symmetries, as well as axionic background fields. The latter are properly interpreted in the context of anomalies in the space of coupling constants.