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

Abstract

We construct explicit compact solutions with non-zero field strength, non-flat instanton and constant dilaton to the heterotic string equations in dimensions 7 and 8. 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 7 and 8. We show that some of our examples are compact supersymmetric solutions of the heterotic equations of motion in dimensions 7 and 8.