Moduli Stabilisation in Heterotic String Compactifications

TL;DR

This paper investigates the structure of supersymmetric vacua in heterotic string compactifications on SU(3) structure manifolds, exploring moduli stabilization and the existence of consistent AdS vacua with potential for gauge unification.

Contribution

It derives effective theories for compactifications on generalized half-flat manifolds, showing their consistency with 4D N=1 supergravity and identifying conditions for stable vacua.

Findings

Supersymmetric vacua are hard to find on half-flat manifolds.

Generalized half-flat manifolds admit consistent supersymmetric AdS vacua.

Approximately 0.1% of vacua have gauge couplings compatible with unification.

Abstract

In this paper we analyze the structure of supersymmetric vacua in compactifications of the heterotic string on certain manifolds with SU(3) structure. We first study the effective theories obtained from compactifications on half-flat manifolds and show that solutions which stabilise the moduli at acceptable values are hard to find. We then derive the effective theories associated with compactification on generalised half-flat manifolds. It is shown that these effective theories are consistent with four-dimensional N=1 supergravity and that the superpotential can be obtained by a Gukov-Vafa-Witten type formula. Within these generalised models, we find consistent supersymmetric (AdS) vacua at weak gauge coupling, provided we allow for general internal gauge bundles. In simple cases we perform a counting of such vacua and find that a fraction of about 1/1000 leads to a gauge coupling consistent with gauge unification.