Non-nilpotent complex geometry of nilmanifolds and heterotic supersymmetry

TL;DR

This paper classifies complex structures on 6-dimensional nilmanifolds and finds new solutions to heterotic supersymmetry equations involving non-zero flux and anomaly cancellation.

Contribution

It provides a classification of non-nilpotent complex structures on 6-nilmanifolds and constructs new heterotic supersymmetry solutions with specific geometric and flux properties.

Findings

Classified non-nilpotent complex structures on 6-nilmanifolds.

Constructed a large family of heterotic supersymmetry solutions.

Found solutions with non-zero flux, non-flat instanton, and constant dilaton.

Abstract

We classify non-nilpotent complex structures on 6-nilmanifolds and their associated invariant balanced metrics. As an application we find a large family of solutions of the heterotic supersymmetry equations with non-zero flux, non-flat instanton and constant dilaton satisfying the anomaly cancellation condition with respect to the Chern connection.