Minkowski spacetime and non-Ricci-flat compactification in heterotic supergravity

TL;DR

This paper finds new non-supersymmetric solutions in heterotic supergravity with compact extra dimensions, involving products of 2-manifolds, which could have phenomenological applications.

Contribution

It introduces explicit non-Ricci-flat, non-supersymmetric solutions in heterotic supergravity with specific product manifolds for extra dimensions.

Findings

Identified three classes of solutions with specific product manifolds.

Explicit metrics for the solutions are constructed.

Solutions are applicable to phenomenological models.

Abstract

We compactify the ten-dimensional spacetime in heterotic supergravity leaving four-dimensional Minkowski spacetime. We search for nonsupersymmetric, non-Ricci-flat solutions of the equations of motion with the quadratic curvature term. By assuming that the extradimensional spaces are products of 2-manifolds, three types of solutions are found. They are $S^2\times T^2 \times H^2/\Gamma$, $S^2\times H^2/\Gamma \times H^2/\Gamma$, and $S^2\times S^2 \times H^2/\Gamma$, where $H^2/\Gamma$ denotes a compact hyperbolic manifold. The metrics can be written explicitly, and they can be applied to phenomenology.