On the Super Higgs Effect in Extended Supergravity

TL;DR

The paper analyzes spontaneous supersymmetry breaking in four-dimensional extended supergravity (no cosmological constant), focusing on how the super Higgs mechanism constrains allowable N→N' reductions through the structure of massless and massive multiplets. By classifying long and short (BPS) multiplets and examining explicit decompositions, it derives nontrivial constraints that exclude several breaking patterns, especially when N−N' is odd. The Scherk-Schwarz mechanism and brane-flux compactifications are presented as robust dynamical realizations of these breakings, with a central role played by abelian translational isometries of the scalar manifolds that account for Goldstone bosons absorbed by vectors. The work links the pattern of vector multiplet masses to the translational structure of the scalar cosets, offering a framework to study realistic hierarchies and guiding future explorations into N→1 scenarios and higher-dimensional extensions.

Abstract

We consider the reduction of supersymmetry in N-extended four dimensional supergravity via the super Higgs mechanism in theories without cosmological constant. We provide an analysis largely based on the properties of long and short multiplets of Poincare' supersymmetry. Examples of the super Higgs phenomenon are realized in spontaneously broken N=8 supergravity through the Scherk-Schwarz mechanism and in superstring compactification in presence of brane fluxes. In many models the massive vectors count the difference in number of the translation isometries of the scalar sigma-model geometries in the broken and unbroken phase.