Heterotic backgrounds via generalised geometry: moment maps and moduli

TL;DR

This paper uses generalised geometry to characterize heterotic backgrounds with minimal supersymmetry, linking geometric structures to supersymmetry conditions, and providing tools to analyze moduli and stability.

Contribution

It introduces a novel geometric framework for heterotic backgrounds using generalised geometry, including superpotential, Kähler potential, and moduli analysis.

Findings

Characterizes heterotic backgrounds with $SU(3)\times Spin(6+n)$ structures.

Provides superpotential and Kähler potential formulations.

Reproduces known cohomologies for moduli spaces.

Abstract

We describe the geometry of generic heterotic backgrounds preserving minimal supersymmetry in four dimensions using the language of generalised geometry. They are characterised by an $SU(3)\times Spin(6+n)$ structure within $O(6,6+n)\times\mathbb{R}^+$ generalised geometry. Supersymmetry of the background is encoded in the existence of an involutive subbundle of the generalised tangent bundle and the vanishing of a moment map for the action of diffeomorphisms and gauge symmetries. We give both the superpotential and the K\"ahler potential for a generic background, showing that the latter defines a natural Hitchin functional for heterotic geometries. Intriguingly, this formulation suggests new connections to geometric invariant theory and an extended notion of stability. Finally we show that the analysis of infinitesimal deformations of these geometric structures naturally reproduces the known cohomologies that count the massless moduli of supersymmetric heterotic backgrounds.