Nearly K\"ahler heterotic compactifications with fermion condensates

TL;DR

This paper explores non-supersymmetric heterotic string compactifications on nearly K"ahler manifolds with flux and fermion condensates, providing a full classification of consistent solutions including both supersymmetric and non-supersymmetric cases.

Contribution

It offers the first explicit solutions to the full equations of motion with fermion condensates on nearly K"ahler manifolds, extending previous supersymmetric analyses.

Findings

New non-supersymmetric solutions identified

Supersymmetric solutions recovered as special cases

Complete classification of heterotic vacua on nearly K"ahler manifolds

Abstract

We revisit AdS_4 heterotic compactifications on nearly K\"ahler manifolds in the presence of H-flux and certain fermion condensates. Unlike previous studies, we do not assume the vanishing of the supersymmetry variations. Instead we determine the full equations of motion originating from the ten-dimensional action, and subsequently we provide explicit solutions to them on nearly K\"ahler manifolds at first order in alpha'. The Bianchi identity is also taken into account in order to guarantee the absence of all anomalies. In the presence of H-flux, which is identified with the torsion of the internal space, as well as of fermion condensates in the gaugino and dilatino sectors, new solutions are determined. These solutions provide a full classification of consistent backgrounds of heterotic supergravity under our assumptions. All the new solutions are non-supersymmetric, while previously known supersymmetric ones are recovered too. Our results indicate that fully consistent (supersymmetric or not) heterotic vacua on nearly K\"ahler manifolds are scarce, even on AdS_4, and they can be completely classified.