6D microstate geometries from 10D structures

TL;DR

This paper employs Generalised Geometry to characterize supersymmetric type II supergravity backgrounds with null Killing vectors, focusing on D1-D5-P microstate geometries, and extends linear solutions to non-linear, regular configurations.

Contribution

It introduces a formalism using Generalised Geometry to analyze supersymmetric backgrounds with null Killing vectors, specifically applied to D1-D5-P microstate geometries.

Findings

Derived equations equivalent to supersymmetry constraints and equations of motion.

Rewritten linear three-charge solution within the new formalism.

Extended linear solutions to non-linear, regular, asymptotically flat configurations.

Abstract

We use the formalism of Generalised Geometry to characterise in general the supersymmetric backgrounds in type II supergravity that have a null Killing vector. We then specify this analysis to configurations that preserve the same supersymmetries as the D1-D5-P system compactified on a four-manifold. We give a set of equations on the forms defining the supergravity background that are equivalent to the supersymmetry constraints and the equations of motion. This study is motivated by the search of new microstate geometries for the D1-D5-P black hole. As an example, we rewrite the linearised three-charge solution of arXiv:hep-th/0311092 in our formalism and show how to extend it to a non-linear, regular and asymptotically flat configuration.