Heterotic supersymmetry, anomaly cancellation and equations of motion

TL;DR

This paper demonstrates that in certain dimensions, heterotic supersymmetry and anomaly cancellation conditions imply the equations of motion if the tangent bundle connection is an instanton, with specific reductions in six dimensions.

Contribution

It establishes the equivalence between supersymmetry, anomaly cancellation, and equations of motion under instanton conditions in multiple dimensions, clarifying the role of the tangent bundle connection.

Findings

In dimensions five to eight, supersymmetry and anomaly cancellation imply equations of motion if the tangent bundle connection is an instanton.

In six dimensions, the connection reduces to a unique SU(3) instanton on stable tangent bundles.

The results specify conditions for heterotic compactifications to satisfy equations of motion.

Abstract

We show that the heterotic supersymmetry (Killing spinor equations) and the anomaly cancellation imply the heterotic equations of motion in dimensions five, six, seven, eight if and only if the connection on the tangent bundle is an instanton. For heterotic compactifications in dimension six this reduces the choice of that connection to the unique SU(3) instanton on a manifold with stable tangent bundle of degree zero.