Self-dual generalized metrics for pure $\mathcal{N}=1$ six-dimensional Supergravity

TL;DR

This paper geometrizes six-dimensional pure algebraic supergravity using Courant algebroids, defining a generalized metric with self-duality conditions, and interprets solutions as generalized self-dual gravitational monopoles.

Contribution

It introduces a novel geometric framework for six-dimensional supergravity via Courant algebroids and generalized metrics, linking solutions to self-dual monopoles.

Findings

Supergravity equations derive from Ricci-flatness of a generalized metric.

Solutions can be viewed as generalized self-dual gravitational monopoles.

Explores controlling singularities in D1-D5 black strings using B-field transformations.

Abstract

We geometrize six-dimensional pure $\mathcal{N}=1$ Supergravity by means of an exact Courant algebroid, whose Severa class is defined through the Supergravity three-form $H$, equipped with a generalized metric and a compatible, torsion-free, generalized connection. The Supergravity equations of motion follow from the vanishing of the Ricci curvature of the generalized metric, satisfying a natural notion of self-duality. This way, we interpret the solutions of six-dimensional pure, $\mathcal{N}=1$, Supergravity as generalized self-dual gravitational monopoles. For the D1-D5 black string solution, we explore the possibility of controlling space-time singularities by using $B$-field transformations.