Brane solutions and integrability: a status report

TL;DR

This paper reviews the current understanding of the integrability of geodesic equations in symmetric coset spaces related to supergravity, focusing on their applications to black hole solutions and branes.

Contribution

It provides a comprehensive status report on the integrability and solvability of geodesic equations in supergravity sigma models, highlighting recent progress and applications.

Findings

Geodesic equations on symmetric coset spaces are integrable in certain supergravity models.

Applications to black hole solutions are emphasized, showing practical relevance.

The review summarizes recent advances in understanding brane solutions through integrability.

Abstract

We review the status of the integrability and solvability of the geodesics equations of motion on symmetric coset spaces that appear as sigma models of supergravity theories when reduced over respectively the timelike and spacelike direction. Such geodesic curves describe respectively timelike and spacelike brane solutions. We emphasize the applications to black holes.