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

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

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.

Finite deformations from a heterotic superpotential: holomorphic Chern--Simons and an $L_\infty$ algebra

We consider finite deformations of the Hull--Strominger system. Starting from the heterotic superpotential, we identify complex coordinates on the off-shell parameter space. Expanding the superpotential around a supersymmetric vacuum leads to a third-order Maurer--Cartan equation that controls the moduli. The resulting complex effective action generalises that of both Kodaira--Spencer and holomorphic Chern--Simons theory. The supersymmetric locus of this action is described by an $L_3$ algebra.

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

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 o…

Solution of heterotic Killing spinor equations and special geometry

We outline the solution of the Killing spinor equations of the heterotic supergravity. In addition, we describe the classification of all half supersymmetric solutions.

三维紧致异形孤子与平行非平凡扭力

Three-dimensional compact Heterotic solitons with parallel torsion

该研究证明了具有平行非平凡扭力的三维紧致异形孤子要么是双曲流形或Heisenberg群商，并给出了标量曲率的上界。

Parallelisable Heterotic Backgrounds

We classify the simply-connected supersymmetric parallelisable backgrounds of heterotic supergravity. They are all given by parallelised Lie groups admitting a bi-invariant lorentzian metric. We find examples preserving 4, 8, 10, 12, 14 and 16 of the 16 supersymmetries.