NS5-branes in IIA supergravity and gravitational anomalies

TL;DR

This paper develops an anomaly-free effective action for IIA supergravity coupled with an NS5-brane, using a Chern-kernel approach to handle singularities and ensure consistency with anomaly cancellation mechanisms.

Contribution

It introduces a novel Chern-kernel method to construct a gravitational-anomaly-free action for IIA supergravity with an NS5-brane, linking it to M5-brane theories via dimensional reduction.

Findings

Constructed an anomaly-free effective action for IIA supergravity with NS5-brane.

Implemented a Chern-kernel approach to manage singularities in the three-form field.

Connected the ten-dimensional action to M5-brane theories through dimensional reduction.

Abstract

We construct a gravitational-anomaly-free effective action for the coupled system of IIA D=10 dynamical supergravity interacting with an NS5-brane. The NS5-brane is considered as elementary in that the associated current is a delta-function supported on its worldvolume. Our approach is based on a Chern-kernel which encodes the singularities of the three-form field strength near the brane in an SO(4)-invariant way and provides a solution for its Bianchi identity in terms of a two-form potential. A dimensional reduction of the recently constructed anomaly-free effective action for an elementary M5-brane in D=11 is seen to reproduce our ten-dimensional action. The Chern-kernel approach provides in particular a concrete realization of the anomaly cancellation mechanism envisaged by Witten.