Duality and Spontaneously Broken Supergravity in Flat Backgrounds

TL;DR

This work develops a unified framework in which spontaneous breaking of extended supergravity in flat backgrounds arises from gauging flat groups that are electric subgroups of the U-duality group $G$. By exploiting different symplectic embeddings, including Scherk–Schwarz reductions and brane-flux compactifications, the authors identify multiple inequivalent gaugings across $N=8$, $N=4$, and $N=2$ theories, yielding vanishing classical cosmological constant and controlled SUSY-breaking patterns. Key contributions include the construction of explicit electric subalgebras for $E_{7,7}$ and related groups, the realization of non-Abelian and Abelian flat groups, and detailed mass spectra with 1/2-BPS and long (non-BPS) gravitino multiplets, along with moduli-space descriptions of broken phases. The results offer a bridge between higher-dimensional compactifications and four-dimensional gauged supergravity, with implications for no-scale models, orientifold flux compactifications, and phenomenologically relevant $N=2 ightarrow N=1$ scenarios, potentially connecting to Randall–Sundrum-like constructions in five dimensions.

Abstract

It is shown that the super Higgs mechanism that occurs in a wide class of models with vanishing cosmological constant (at the classical level) is obtained by the gauging of a flat group which must be an electric subgroup of the duality group. If the residual massive gravitinos which occur in the partial supersymmetry breaking are BPS saturated, then the flat group is non abelian. This is so for all the models obtained by a Scherk-Schwarz supersymmetry breaking mechanism. If gravitinos occur in long multiplets, then the flat groups may be abelian. This is the case of supersymmetry breaking by string compactifications on an orientifold T^6/Z_2 with non trivial brane fluxes.