Supersymmetric heterotic string backgrounds

TL;DR

This paper classifies supersymmetric backgrounds in heterotic string theory by analyzing Killing spinor equations, extending previous work on type I backgrounds, and provides a comprehensive understanding of geometric and gauge conditions.

Contribution

It applies and extends previous classifications to heterotic strings, solving key Killing spinor equations and classifying supersymmetry conditions in ten-dimensional gauge theory.

Findings

Classification of heterotic string backgrounds based on Killing spinor equations

Explicit solutions to gaugino, gravitino, and dilatino equations

Comprehensive supersymmetry conditions for ten-dimensional gauge theory

Abstract

We present the main features of the solution of the gravitino and dilatino Killing spinor equations derived in hep-th/0510176 and hep-th/0703143 which have led to the classification of geometric types of all type I backgrounds. We then apply these results to the supersymmetric backgrounds of the heterotic string. In particular, we solve the gaugino Killing spinor equation together with the other two Killing spinor equations of the theory. We also use our results to classify all supersymmetry conditions of ten-dimensional gauge theory.