Gaugino Condensates and Fluxes in N = 1 Effective Superpotentials

TL;DR

The work studies how fluxes and gaugino condensates shape $N=1$ effective superpotentials in heterotic and type II orientifolds, leveraging $N=4$ gaugings to fix the flux-induced superpotential for the $S,T_A,U_A$ moduli. It shows that nonperturbative gaugino-condensation effects, modeled via a composite field and Veneziano–Yankielowicz structure, interact with flux terms to stabilize moduli and control SUSY breaking, with vacua ranging from no-scale, to SUSY-breaking Minkowski, to AdS depending on the balance of perturbative and nonperturbative contributions. The paper identifies three gravitino-mass scaling regimes—set by whether SUSY breaking is flux-driven, nonperturbatively induced, or directly caused by gaugino condensation in heterotic contexts—and demonstrates through explicit Type IIA and heterotic examples how to avoid runaway behavior. Overall, it emphasizes the necessity of treating the full superpotential, including both flux-induced and condensate terms, to obtain viable moduli stabilization and SUSY-breaking phenomenology in string-inspired $N=1$ theories.

Abstract

In the framework of orbifold compactifications of heterotic and type II orientifolds, we study effective N = 1 supergravity potentials arising from fluxes and gaugino condensates. These string solutions display a broad phenomenology which we analyze using the method of N = 4 supergravity gaugings. We give examples in type II and heterotic compactifications of combined fluxes and condensates leading to vacua with naturally small supersymmetry breaking scale controlled by the condensate, cases where the supersymmetry breaking scale is specified by the fluxes even in the presence of a condensate and also examples where fluxes and condensates conspire to preserve supersymmetry.