Kodaira-Spencer theory for flux backgrounds

TL;DR

This paper constructs a holomorphic theory for supersymmetric backgrounds in ten-dimensional supergravity, extending BCOV theory and connecting to Courant algebroids, with potential implications for understanding supergravity twists.

Contribution

It provides an explicit component field description of a holomorphic theory for supergravity backgrounds, generalising existing models and linking to Courant algebroid structures.

Findings

Explicit component field description of the holomorphic supergravity theory.

Connection between the theory and Courant contact models.

Reproduction of recent constrained field models via coisotropic reduction.

Abstract

We give an explicit description (in component fields) of a holomorphic theory associated to a general supersymmetric background of $\mathcal N=1$ supergravity in ten dimensions. Conjecturally, this provides a sought-for holomorphic realisation of the supergravity twist in such backgrounds, generalising the minimal type I BCOV theory for Calabi-Yau manifolds. Our theory unpacks the recently introduced Courant contact model associated to a holomorphic Courant algebroid. We also show that a coisotropic reduction of this model reproduces the recent model of ref [1], which is formulated in terms of constrained fields.