Dimensional Reduction of the Heterotic String over nearly-Kaehler manifolds

TL;DR

This paper derives the four-dimensional effective action from ten-dimensional heterotic supergravity compactified on nearly-Kähler manifolds, using coset space dimensional reduction and analyzing scalar potentials and supergravity descriptions.

Contribution

It provides a detailed reduction scheme over non-symmetric coset spaces and explicitly derives the scalar potentials and supergravity formulations for nearly-Kähler compactifications.

Findings

Derived four-dimensional scalar potentials for all three non-symmetric coset spaces.

Established the supergravity description using heterotic Gukov-Vafa-Witten formula.

Analyzed the nearly-Kähler limit within the reduction scheme.

Abstract

Our aim is to derive the effective action in four dimensions resulting by reducing dimensionally the ten-dimensional ${\cal N}=1$ heterotic supergravity coupled to ${\cal N}=1$ super Yang-Mills over manifolds admitting a nearly-K\"{a}hler structure. Given the fact that all six-dimensional nearly-K\"{a}hler manifolds are included in the class of the corresponding non-symmetric coset spaces plus a group manifold, our procedure amounts in applying the Coset Space Dimensional Reduction scheme using these coset spaces as internal manifolds. In our examination firstly the rules of the reduction of the theory over a general six-dimensional non-symmetric manifold are stated and subsequently a detailed case by case analysis is performed for all the three non-symmetric coset spaces. For each case the four-dimensional scalar potential is derived and the corresponding nearly-K\"{a}hler limit is obtained. Finally, we determine the corresponding supergravity description of the four-dimensional theory employing the heterotic Gukov-Vafa-Witten formula and results of the special K\"{a}hler geometry.