Higgs and super-Higgs effects with naturally vanishing classical 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 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.

Aspects of spontaneously broken N = 1 global supersymmetry in the presence of gauge interactions

“…Similarly to the cases discussed in previous sections, also the more general models under consideration admit a simple and interesting embedding in supergravity models with spontaneously broken supersymmetry and vanishing vacuum energy. Adapting the analysis of [11] to the present case, we find that an underlying supergravity model can be defined via the SO(2, N)/SO(2) × SO(N) Kähler potential…”

“…supergravity, such an approach was previously studied in refs. [30,31,11]. We recall that, in the presence of gravitational interactions, the additional property of vanishing vacuum energy can be fulfilled at the same time.…”

“…If Λ S ≪ v, then the supersymmetry-breaking mass splittings are much smaller than the scale of gauge symmetry breaking, and the interactions induced by the superpotential are strongly suppressed by positive powers of Λ S /v. An obvious physical application would be to identify the broken gauge group with some grand-unified group, as already attempted elsewhere [30,11] in the supergravity context: the scale of supersymmetry breaking would then be Λ S ∼ G…”

“…We also show how this model can be obtained from a supergravity model with vanishing vacuum energy, previously studied in ref. [11], by taking the appropriate flat limit. We then discuss how the scales Λ S and v, associated with supersymmetry and gauge symmetry breaking, respectively, control the spectrum and the interactions, and show that Λ S ≫ v would lead to a premature violation of treelevel unitarity and correspond to a strong coupling régime.…”

Low-scale supersymmetry breaking: effective description, electroweak breaking and phenomenology

“…We recall that, upon electroweak breaking, the goldstino can also have components along neutral gauginos, for nonvanishing D a . However, such components do not contribute to the coupling of A a µ to goldstino bilinears 24 . This could give the impression that the Z-goldstino-goldstino coupling is only determined by F -breaking, with electroweak D-breaking playing no role.…”