Supersymmetry breaking, heterotic strings and fluxes

TL;DR

This paper explores heterotic string compactifications with background fluxes on a specific geometric setup, analyzing how different flux choices affect supersymmetry preservation and solving related differential equations for the dilaton.

Contribution

It provides a detailed analysis of flux compactifications on a T^2 fibration over K3, including the derivation and solvability of the dilaton's differential equation for N=2 supersymmetry.

Findings

Supersymmetry preservation depends on flux choices.

The dilaton equation reduces to a Laplace-type equation for N=2 cases.

Solvability of the dilaton equation is guaranteed in the N=2 scenario.

Abstract

In this paper we consider compactifications of heterotic strings in the presence of background flux. The background metric is a T^2 fibration over a K3 base times four-dimensional Minkowski space. Depending on the choice of three-form flux different amounts of supersymmetry are preserved (N=2,1,0). For supersymmetric solutions unbroken space-time supersymmetry determines all background fields except one scalar function which is related to the dilaton. The heterotic Bianchi identity gives rise to a differential equation for the dilaton which we discuss in detail for solutions preserving an N=2 supersymmetry. In this case the differential equation is of Laplace type and as a result the solvability is guaranteed.