Non-Kaehler Heterotic String Compactifications with non-zero fluxes and constant dilaton

Understand

We construct new explicit compact supersymmetric valid solutions with non-zero field strength, non-flat instanton and constant dilaton to the heterotic equations of motion in dimension six.

• We present balanced Hermitian structures on compact nilmanifolds in dimension six satisfying the heterotic supersymmetry equations with non-zero flux, non-flat instanton and constant dilaton which obey the three-form Bianchi identity with curvature term taken with respect to either the Levi-Civita, the (+)-connection or the Chern connection.
• Among them, all our solutions with respect to the (+)-connection on the compact nilmanifold $M_3$ satisfy the heterotic equations of motion.