# Dirac branes for Dirichlet branes: Supergravity actions

## TL;DR

This paper extends Dirac's string formalism to D-branes in type IIA and IIB supergravity, providing new derivations of brane-induced Chern-Simons terms and clarifying the role of Dirac branes in massive IIA theory.

## Contribution

It introduces a novel approach to handle magnetic sources in supergravity by treating gauge potentials as sections and extends Dirac's formalism to D-branes, including a noncovariant formulation of IIB theory.

## Key findings

- Derived brane-induced Chern-Simons terms in supergravity actions.
- Provided a prescription for integrating over potentials with magnetic sources.
- Showed how D8-branes source the mass parameter in IIA supergravity.

## Abstract

Nontrivial Bianchi identities with local magnetic sources are solved by recognizing that gauge potentials are sections rather than globally defined functions, but properly accounting for the source degrees of freedom requires a modification of the field strength. Following work by Teitelboim and by Cariglia and Lechner, we extend Dirac's string formalism for monopoles to D-branes in type IIA and IIB string theory. We give novel derivations of brane-induced Chern-Simons terms in the supergravity actions, including a prescription for integrating over potentials in the presence of magnetic sources. We give a noncovariant formulation of the IIB theory, keeping only the independent degrees of freedom of the self-dual 4-form potential. Finally, it is well-known that D8-branes source the mass parameter of IIA supergravity; we show that the additional couplings of the massive IIA supergravity, including on other D-brane worldvolumes, are a consequence of the corresponding Dirac branes.