Anomaly-induced vanishing of brane partition functions

TL;DR

This paper explores how 't Hooft anomalies cause the vanishing of certain brane partition functions, revealing deep connections between anomalies, higher-form symmetries, and brane physics.

Contribution

It generalizes the understanding of anomaly-induced partition function vanishing to higher-form symmetries and applies this to derive anomaly cancellation conditions for M5- and D3-branes.

Findings

Partition functions vanish in the presence of background charges due to anomalies.

Derived anomaly cancellation conditions for M5-branes and D3-branes in specific backgrounds.

Extended the anomaly analysis to higher-form symmetries beyond traditional cases.

Abstract

In the presence of 't Hooft anomalies, backgrounds for the symmetries of a quantum field theory can lead to non-conservation of Noether currents, or more generally, to the presence of charged insertions in the path integral. When there is a net background charge, the partition function evaluated on closed manifolds will vanish. For anomalous symmetries, this statement can also be understood as the anomaly theory giving rise to a non-trivial anomalous phase for the partition function even for "rigid" transformations which leave all background fields unchanged. We use the generalisation of this second viewpoint to the setting of anomalous higher-form symmetries in order to show vanishing of the partition function for a number of examples, both with and without a Lagrangian description. In particular, we show how to derive from these considerations the analogue of the Freed-Witten anomaly cancellation condition for the M5-brane, and also that for the D3-brane in S-fold backgrounds.