Supergravities on Branes

TL;DR

This paper extends known brane-worldvolume Kaluza-Klein reductions from flat to full nonlinear supergravity theories for D3- and M5-branes, enabling consistent embeddings of lower-dimensional supergravity solutions.

Contribution

It introduces a method to embed full nonlinear supergravity theories on branes, extending previous flat-worldvolume truncations to more complete supergravity models.

Findings

Extended brane-worldvolume supergravity truncations to nonlinear theories.

Maintained supersymmetry consistent with original flat branes.

Provided explicit examples of embedded supergravity solutions.

Abstract

Supergravity brane solutions allow for a generalised type of Kaluza-Klein reduction onto brane worldvolumes. The known replacement of a flat worldvolume metric by a Ricci-flat metric constitutes a consistent Kaluza-Klein truncation of the starting higher-dimensional supergravity theory down to a lower-dimensional pure gravity theory. This paper shows how to extend such a brane-worldvolume pure-gravity consistent truncation to that for a full nonlinear supergravity theory for the Type IIB D3-brane and the M-theory/Type IIA M5-brane. The extension of worldvolume supersymmetry is given by the unbroken supersymmetry of the original flat "skeleton" brane. Compatibility with further worldvolume diagonal and transverse vertical dimensional reductions is also shown, providing the brane-worldvolume supergravity embeddings of all descendants of the skeleton D3- and M5-branes. Examples are given of brane-worldvolume supergravity solutions embedded into the corresponding higher-dimensional supergravities.