Supersymmetry breaking, heterotic strings and fluxes

TL;DR

The paper analyzes heterotic string compactifications with background NS flux on a $T^2$ fibration over a K3 base, linking flux choices to 4D supersymmetry and deriving the dilaton equation from the heterotic Bianchi identity. By first reviewing Type IIB backgrounds and the corresponding dual heterotic setup, the authors derive leading-order and $O(\alpha')$ corrected equations, including explicit expressions for $\mathrm{tr}(R_+\wedge R_+)$ and the (2,2) nature of the curvature, which render the dilaton equation Laplace-type and solvable in the N=2 case. They show how different flux components enforce varying amounts of SUSY (N=2, N=1, N=1', N=0) and discuss the structure of the corrected N=2 background, including warp-factor redefinitions that preserve supersymmetry. The results demonstrate the solvability of the Bianchi identity with $O(\alpha')$ corrections and provide a concrete framework for constructing compact, torsional heterotic geometries with controlled quantum corrections and potential phenomenological implications.

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.