Five-Brane Effective Action In M-Theory

TL;DR

This paper addresses the challenge of defining the partition function for the self-dual two-form on M-theory five-branes, providing a resolution and analyzing anomaly cancellation in this context.

Contribution

It presents a framework for the partition function of the self-dual field on M5-branes and offers a detailed analysis of anomaly cancellation mechanisms.

Findings

Resolution of the partition function problem for the self-dual field

Insights into anomaly cancellation on M5-branes

Comparison with similar issues in Type IIB superstring theory

Abstract

On the world-volume of an $M$-theory five-brane propagates a two-form with self-dual field strength. As this field is non-Lagrangian, there is no obvious framework for determining its partition function. An analogous problem exists in Type IIB superstring theory for the self-dual five-form. The resolution of these problems and definition of the partition function is explained. A more complete analysis of perturbative anomaly cancellation for $M$-theory five-branes is also presented, uncovering some surprising details.