CERN-PH-TH/2013-234

Vacuum structure in a chiral modification of pure supergravity

[1.5cm] Sergio Ferrara, Alex Kehagias and Massimo Porrati

[1.1cm]

Physics Department, Theory Unit, CERN, CH 1211, Geneva 23, Switzerland

INFN - Laboratori Nazionali di Frascati, Via Enrico Fermi 40, I-00044 Frascati, Italy

Physics Division, National Technical University of Athens, 15780 Zografou Campus, Athens, Greece

Department of Theoretical Physics 24 quai E. Ansermet, CH-1211 Geneva 4, Switzerland

CCPP, Department of Physics, NYU 4 Washington Pl. New York NY 10016, USA

Abstract

[0.5cm]

We discuss an class of modified , supergravity models where the deformation is a monomial in the chiral scalar curvature multiplet of the “old minimal” auxiliary field formulation. The scalaron and goldstino multiplets are dual to each other in this theory. Since one of them is not dynamical, this theory, as recently shown, cannot be used as the supersymmetric completion of gravity. This is confirmed by investigating the scalar potential and its critical points in the dual standard supergravity formulation with a single chiral multiplet with specific Kähler potential and superpotential. We study the vacuum structure of this dual theory and we find that there is always a supersymmetric Minkowski critical point which however is pathological for as it corresponds to a corner () and a cusp () point of the potential. For an anti-de Sitter regular supersymmetric vacuum emerges. As a result, this class of models are not appropriate to describe inflation. We also find the mass spectrum and we provide a general formula for the masses of the scalars of a chiral multiplet around the anti-de Sitter critical point and their relation to unitary representations.