Infinitesimal moduli for the Strominger system and Killing spinors in generalized geometry

TL;DR

This paper develops a mathematical framework to analyze small variations of solutions to the Strominger system, linking generalized geometry and moduli space structure, with applications to special holonomy metrics.

Contribution

It constructs the infinitesimal moduli space and obstruction space for the Strominger system using elliptic operators, and explores the geometry of the moduli space and its relation to Killing spinors.

Findings

Description of the infinitesimal structure of the moduli space

Identification of a foliation related to generalized geometry

A unifying framework for $ ext{SU}(3)$ holonomy metrics and Strominger solutions

Abstract

We construct the space of infinitesimal variations for the Strominger system and an obstruction space to integrability, using elliptic operator theory. We initiate the study of the geometry of the moduli space, describing the infinitesimal structure of a natural foliation on this space. The associated leaves are related to generalized geometry and correspond to moduli spaces of solutions of suitable Killing spinor equations on a Courant algebroid. As an application, we propose a unifying framework for metrics with holonomy $\SU(3)$ and solutions of the Strominger system.