Heterotic compactifications on nearly K\"ahler manifolds

TL;DR

This paper explores heterotic supergravity compactifications on nearly Kähler manifolds, confirming supersymmetry and equations of motion with string corrections, and presents both supersymmetric and non-supersymmetric models with fixed internal space volume.

Contribution

It completes a model on SU(3)/U(1)xU(1) by verifying supersymmetry and equations of motion, and introduces a non-supersymmetric solution, confirming recent theoretical results.

Findings

Supersymmetric model satisfies equations of motion with alpha' corrections.

Non-supersymmetric model also satisfies the equations.

Internal space volume is fixed by the constraints.

Abstract

We consider compactifications of heterotic supergravity on anti-de Sitter space, with a six-dimensional nearly K"ahler manifold as the internal space. Completing the model proposed by Frey and Lippert with the particular choice of SU(3)/U(1)xU(1) for the internal manifold, we show that it satisfies not only the supersymmetry constraints but also the equations of motion with string corrections of order alpha'. Furthermore, we present a non-supersymmetric model. In both solutions we find confirmed a recent result of Ivanov on the connection used for anomaly cancellation. Interestingly, the volume of the internal space is fixed by the supersymmetry constraints and/or the equations of motion.