Gaugino Condensation and SUSY Breakdown

TL;DR

This work analyzes gaugino condensation as a mechanism for hidden-sector SUSY breaking and moduli stabilization within the heterotic string and Horava–Witten M-theory frameworks. By connecting gaugino bilinears to higher-dimensional $H$-flux and exploiting anomaly-cancellation structures, it derives the 4D effective action, including moduli ($S,T$) and charged fields, and shows how gaugino condensation can dynamically set the vacuum energy while inducing SUSY breaking primarily through the $F$-term of the ${\cal T}$ modulus. In the strongly coupled regime, the HOřava–Witten construction yields calculable 4D effective actions with wall-localized SUSY breaking, gravitino masses $m_{3/2}\sim\Lambda^3/M_{Pl}^2$, and soft terms transmitted to the visible sector, with gauge couplings controlled by $f_6$ and $f_8$ becoming $f_6={\cal S}+\alpha{\cal T}$ and $f_8={\cal S}-\alpha{\cal T}$. The paper highlights the interplay between nonperturbative dynamics, fluxes, and higher-dimensional consistency conditions as central to moduli stabilization and realistic SUSY phenomenology, while noting open issues such as full moduli stabilization, loop corrections, and the cosmological constant. Overall, it provides a coherent framework linking 10D/11D supergravity, compactification, and nonperturbative dynamics to SUSY breaking and low-energy physics.

Abstract

We review the mechanism of gaugino condensation in the framework of the $d=10$ heterotic string and its $d=11$ extension of Horava and Witten. In particular we emphasize the relation between the gaugino condensate and the flux of the antisymmetric tensor fields of higher dimensional supergravity. Its potential role for supersymmetry breakdown and moduli stabilization is investigated.