Compact supersymmetric solutions of the heterotic equations of motion in dimensions 7 and 8

TL;DR

This paper constructs explicit compact solutions to heterotic string equations in 7 and 8 dimensions, satisfying supersymmetry and anomaly cancellation, with non-zero field strength and constant dilaton.

Contribution

It provides a quadratic curvature condition that ensures heterotic supersymmetry and anomaly cancellation imply the equations of motion in these dimensions.

Findings

Explicit compact solutions with non-zero field strength and constant dilaton.

A quadratic curvature condition linking supersymmetry, anomaly cancellation, and equations of motion.

Examples of compact supersymmetric solutions in 7 and 8 dimensions.

Abstract

We construct explicit compact solutions with non-zero field strength, non-flat instanton and constant dilaton to the heterotic string equations in dimensions seven and eight. We present a quadratic condition on the curvature which is necessary and sufficient the heterotic supersymmetry and the anomaly cancellation to imply the heterotic equations of motion in dimensions seven and eight. We show that some of our examples are compact supersymmetric solutions of the heterotic equations of motion in dimensions seven and eight.