Reducing the Heterotic Supergravity on nearly-Kahler coset spaces

TL;DR

This paper explores the dimensional reduction of ten-dimensional heterotic supergravity on nearly-Kähler coset spaces, deriving four-dimensional supergravity theories with potential for chiral fermions and analyzing their vacua.

Contribution

It provides the first detailed reduction of heterotic supergravity on non-symmetric coset spaces, leading to new four-dimensional no-scale supergravity models.

Findings

Derived effective four-dimensional supergravity actions.

Identified conditions for chiral fermions with gauge fields.

Analyzed vacuum structure of the resulting theories.

Abstract

We study the dimensional reduction of the ${\cal N}=1$, ten-dimensional Heterotic Supergravity to four dimensions, at leading order in $\alpha'$, when the internal space is a nearly-K\"{a}hler manifold. Nearly-K\"{a}hler manifolds in six dimensions are all the non-symmetric coset spaces and a group manifold. Here we reduce the theory using as internal manifolds the three six-dimensional non-symmetric coset spaces, omitting the case of the group manifold in the prospect of obtaining chiral fermions when the gauge fields will be included. We determine the effective actions for these cases, which turn out to describe ${\cal N}=1$ four-dimensional supergravities of the no-scale type and we study the various possibilities concerning their vacuum.