Gaugino condensation and the anomalous $U(1)$

TL;DR

Addresses the effect of an anomalous $U(1)_X$ on gaugino condensation and dynamical SUSY breaking in string-inspired models. The authors build a concrete hidden-sector model with gauge group $SU(N_c)\times U(1)_X$ and $N_f\le N_c$ flavors, incorporating a Fayet-Iliopoulos term and Green-Schwarz cancellation, and show that a SUSY-breaking ground state arises from the interplay of two scales, $\xi$ and $\Lambda$. They derive the ground-state structure and compute the soft-breaking terms, finding tree-level scalar masses and A-terms tied to $\langle D_X\rangle$ and $\langle F_\phi/\phi\rangle$, and hidden-sector gaugino masses $m_\lambda\sim N_f\langle F_M/M\rangle$, with visible gauginos generated at loop level. The results highlight a linked role for the scales and predict positive scalar masses ($D_X>0$) and a suppressed gravitino mass, with SUSY restored in the limits $\Lambda\to0$ or $\xi\to\infty$.

Abstract

We study gaugino condensation in presence of an anomalous $U(1)$ gauge group and find that global supersymmetry is dynamically broken. An example of particular interest is provided by effective string models with 4-dimensional Green-Schwarz anomaly cancellation mechanism. The structure of the hidden sector is constrained by the anomaly cancellation conditions and the scale of gaugino condensation is shifted compared with the usual case. We explicitly compute the resulting soft supersymmetry breaking terms.