Supergravity as Generalised Geometry I: Type II Theories

TL;DR

This paper reformulates ten-dimensional type II supergravity using generalised geometry, providing a new geometric framework that simplifies the action, equations of motion, and supersymmetry variations in a covariant form.

Contribution

It introduces a generalised geometric formulation of type II supergravity, defining a new analogue of the Levi-Civita connection and curvature within this framework.

Findings

Rewrites supergravity action and equations in a covariant form

Defines a generalised Levi-Civita connection and curvature

Simplifies supersymmetry variations in the new geometric setting

Abstract

We reformulate ten-dimensional type II supergravity as a generalised geometrical analogue of Einstein gravity, defined by an $O(9,1)\times O(1,9)\subset O(10,10)\times\mathbb{R}^+$ structure on the generalised tangent space. Using the notion of generalised connection and torsion, we introduce the analogue of the Levi-Civita connection, and derive the corresponding tensorial measures of generalised curvature. We show how, to leading order in the fermion fields, these structures allow one to rewrite the action, equations of motion and supersymmetry variations in a simple, manifestly $\mathit{Spin}(9,1)\times\mathit{Spin}(1,9)$-covariant form.