Heterotic Solutions with G2 and Spin(7) Structures

TL;DR

This paper explores supersymmetric solutions in 7- and 8-dimensional heterotic supergravity, deriving explicit metrics with special holonomy and torsion, expanding understanding of geometric structures in string theory.

Contribution

It provides explicit constructions of ALC metrics with $G_2$ and $Spin(7)$ structures, including solutions with specific singularities, using differential equations derived from torsion conditions.

Findings

Explicit ALC metrics with $S^{3}$-bolt and $T^{1,1}$-bolt singularities.

Solutions characterized by torsion equations on $G_2$ and $Spin(7)$ manifolds.

Methodology applicable to other special holonomy and torsion-related problems.

Abstract

We study supersymmetric solutions in 7- and 8-dimensional Abelian heterotic supergravity theories. In dimension 7, the solutions are described by $G_{2}$ with torsion equations. When a $G_{2}$ manifold has principal orbits $S^{3} \times S^{3}$, the equations are reduced to ordinary differential equations with four radial functions. For these equations we obtain explicit ALC metrics with $S^{3}$-bolt and $T^{1,1}$-bolt singularities. In dimension 8, we study supersymmetric solutions to $Spin(7)$ with torsion equations associated with 3-Sasakian manifolds by using a similar method to the case $G_{2}$.