A note on the M5 brane anomaly

TL;DR

This paper investigates the M5 brane anomaly cancellation by reformulating existing constructions, proposing a new magnetic coupling solution, and demonstrating its consistency with supergravity and anomaly inflow mechanisms.

Contribution

It introduces a novel magnetic coupling solution that aligns with supergravity and simplifies anomaly cancellation without requiring SO(5) variation of the 3-form.

Findings

The new solution matches the supergravity M5 brane outside the core.

It reproduces the same anomaly inflow as FHMM construction.

The reformulation clarifies the relation between anomaly cancellation and supergravity solutions.

Abstract

The problem of the M5 brane anomaly cancellation is addressed. We reformulate FHMM construction making explicit the relation with the M5 brane SUGRA solution. We suggest another solution to the magnetic coupling equation which doesn't need anomalous SO(5) variation of the 3-form potential and coincides with the SUGRA solution outside smoothed out core of the magnetic source. Chern-Simons term evaluated on this solution generates the same anomaly inflow as achieved by FHMM.