Higgs and super-Higgs effects with naturally vanishing vacuum energy

Abstract

We construct $N=1$ supergravity models where the gauge symmetry and supersymmetry are both spontaneously broken, with naturally vanishing classical vacuum energy and unsuppressed Goldstino components along gauge non-singlet directions. We discuss some physically interesting situations where such a mechanism could play a role, and identify the breaking of a grand-unified gauge group as the most likely possibility. We show that, even when the gravitino mass is much smaller than the scale $m_X$ of gauge symmetry breaking, important features can be missed if we first naively integrate out the degrees of freedom of mass ${\cal O} (m_X)$, in the limit of unbroken supersymmetry, and then describe the super-Higgs effect in the resulting effective theory. We also comment on possible connections with extended supergravities and realistic four-dimensional string constructions.