BPS Action and Superpotential for Heterotic String Compactifications with Fluxes

TL;DR

The paper addresses the challenge of moduli stabilization in heterotic string compactifications with fluxes by showing that, up to ${O(α'^2)}$, the ten-dimensional action can be rewritten as a sum of squares of BPS-like quantities. This structure guarantees that backgrounds solving the Strominger-type SUSY conditions and the modified Bianchi identity also solve the equations of motion, providing a robust link between SUSY geometry and dynamics. The authors propose a heterotic analog of the Gukov-type superpotential, $W=igintss {oldsymbol{𝓗}amily Ω}$ with ${oldsymbol{𝓗}}=H+rac{i}{2}e^{-8φ}d(e^{8φ}J)$, whose extremization enforces torsional constraints that lock the flux to the almost complex structure. They further discuss radial modulus stabilization and the limitations posed by higher-order ${α'}$ corrections, highlighting the subtleties of flux backgrounds on SU(3) structures and the potential breakdown of the supergravity approximation in certain regimes.

Abstract

We consider N =1 compactifications to four dimensions of heterotic string theory in the presence of fluxes. We show that up to order O(α'^2) the associated action can be written as a sum of squares of BPS-like quantities. In this way we prove that the equations of motion are solved by backgrounds which fulfill the supersymmetry conditions and the Bianchi identities. We also argue for the expression of the related superpotential and discuss the radial modulus stabilization for a class of examples.