G-structures and Domain Walls in Heterotic Theories

TL;DR

This paper studies heterotic string solutions involving warped products of four-dimensional domain walls and six-dimensional manifolds with SU(3) structure, identifying the specific geometric constraints and including known solutions as special cases.

Contribution

It derives the conditions on internal manifolds with SU(3) structure for heterotic solutions, introducing generalized half-flat manifolds with specific torsion patterns.

Findings

Internal manifolds are generalized half-flat with specific torsion classes.

Previous heterotic compactifications on half-flat mirror manifolds fit within this framework.

The solutions preserve two supercharges and include Strominger's complex non-Kahler manifolds.

Abstract

We consider heterotic string solutions based on a warped product of a four-dimensional domain wall and a six-dimensional internal manifold, preserving two supercharges. The constraints on the internal manifolds with SU(3) structure are derived. They are found to be generalized half-flat manifolds with a particular pattern of torsion classes and they include half-flat manifolds and Strominger's complex non-Kahler manifolds as special cases. We also verify that previous heterotic compactifications on half-flat mirror manifolds are based on this class of solutions.