Higgs in nilpotent supergravity: Vacuum energy and Festina Lente

Abstract

In this note we study supergravity models with constrained superfields. We construct a supergravity framework in which all (super)symmetry breaking dynamics happen in vacuum with naturally (or otherwise asymptotically) vanishing energy. Supersymmetry is generically broken in multiple sectors each of them is parametrized by a nilpotent goldstino superfield. Dynamical fields (the Higgs, inflaton, etc) below the supersymmetry breaking scale are constrained superfields of various types. In this framework, there is a dominant supersymmetry breaking sector which uplifts the potential to zero value. Other sources of supersymmetry breaking have (asymptotically) vanishing contribution to vacuum energy such that supersymmetry is locally restored. Demanding vanishing vacuum energy constrains the structure of the superpotential and Kahler potential; there is a superpotential term for each secluded sector directly interacting with a nilpotent superfield and the Kahler potential must have a shift symmetry along Higgs field directions. This structure is inspired by elements that appear in string theory. We also study the Higgs dynamics during inflation and show that the swampland Festina Lente bound could be realized in this framework.