Heterotic on Half-flat

TL;DR

This paper investigates the effective action of heterotic string theory compactified on half-flat manifolds, deriving the superpotential and Kahler potential, and exploring the role of intrinsic geometric flux and gauge fields.

Contribution

It explicitly derives the superpotential and Kahler potential for heterotic compactifications on half-flat manifolds, introducing new flux-dependent terms and a generalized Gukov formula for SU(3) structure manifolds.

Findings

Derived superpotential with flux-dependent terms

Established a generalized Gukov formula for SU(3) structure

Confirmed superpotential consistency with explicit calculations

Abstract

We study the effective action of the heterotic string compactified on particular half-flat manifolds which arise in the context of mirror symmetry with NS-NS flux. We explicitly derive the superpotential and Kahler potential at lowest order in alpha' by a reduction of the bosonic action. The superpotential contains new terms depending on the Kahler moduli which originate from the intrinsic geometrical flux of the half-flat manifolds. A generalized Gukov formula, valid for all manifolds with SU(3) structure, is derived from the gravitino mass term. For the half-flat manifolds it leads to a superpotential in agreement with our explicit bosonic calculation. We also discuss the inclusion of gauge fields.