Compact supersymmetric solutions of the heterotic equations of motion in dimension 5

TL;DR

This paper constructs explicit compact supersymmetric solutions in five-dimensional heterotic string theory, satisfying supersymmetry, anomaly cancellation, and equations of motion with non-zero fluxes and constant dilaton.

Contribution

It provides a new class of explicit compact solutions in dimension five that meet all heterotic string theory conditions, including a quadratic curvature condition.

Findings

Constructed explicit compact solutions with non-zero fluxes

Established a quadratic curvature condition for solutions

Provided examples on compact nilmanifolds in dimension five

Abstract

We construct explicit compact supersymmetric solutions with non-zero field strength, non-flat instanton and constant dilaton to the heterotic string equations in dimension five. 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 dimension five. We supply compact nilmanifold in dimension 5 satisfying the heterotic supersymmetry equations with non-zero fluxes and constant dilaton which obey the three-form Bianchi identity and solves the heterotic equations of motion in dimension five.