Heterotic G_2-manifold compactifications with fluxes and fermionic condensates

TL;DR

This paper explores flux compactifications of heterotic string theory on 7-manifolds with G_2-structure, solving the field equations with fermionic condensates, but finds no supersymmetric solutions.

Contribution

It provides explicit solutions to heterotic flux compactifications with fermionic condensates on G_2-structured manifolds, including non-standard embeddings, and analyzes their supersymmetry properties.

Findings

Solutions satisfy all field equations and Bianchi identity to order alpha'

None of the solutions preserve supersymmetry

Gauge fields chosen as G_2-instantons for anomaly cancellation

Abstract

We consider flux compactifications of heterotic string theory in the presence of fermionic condensates on M_{1,2} times X_7 with both factors carrying a Killing spinor. In other words, M_{1,2} is either de Sitter, anti-de Sitter or Minkowski, and X_7 possesses a nearly parallel G_2-structure or has G_2-holonomy. We solve the complete set of field equations and the Bianchi identity to order alpha'. The latter is satisfied via a non-standard embedding by choosing the gauge field to be a G_2-instanton. It is shown that none of the solutions to the field equations is supersymmetric.