Superconformal Symmetry, NMSSM, and Inflation

TL;DR

This paper introduces a class of supergravity models with superconformal symmetry that embed scale-invariant theories like NMSSM, enabling natural solutions to hierarchy and cosmological problems while facilitating inflation within supergravity.

Contribution

It presents the canonical superconformal supergravity (CSS) models that embed scale-invariant theories into supergravity, linking superconformal symmetry to phenomenological issues like the  problem and inflation.

Findings

Scale-free scalar potentials are preserved after supergravity embedding.

The models provide natural solutions to the  problem and domain wall issues.

New versions of chaotic inflation compatible with supergravity are proposed.

Abstract

We identify a particularly simple class of supergravity models describing superconformal coupling of matter to supergravity. In these models, which we call the canonical superconformal supergravity (CSS) models, the kinetic terms in the Jordan frame are canonical, and the scalar potential is the same as in the global theory. The pure supergravity part of the total action has a local Poincare supersymmetry, whereas the chiral and vector multiplets coupled to supergravity have a larger local superconformal symmetry. The scale-free globally supersymmetric theories, such as the NMSSM with a scale-invariant superpotential, can be naturally embedded into this class of theories. After the supergravity embedding, the Jordan frame scalar potential of such theories remains scale free; it is quartic, it contains no mass terms, no nonrenormalizable terms, no cosmological constant. The local superconformal symmetry can be broken by additional terms, which, in the small field limit, are suppressed by the gravitational coupling. This can be achieved by introducing the nonminimal scalar-curvature coupling, and by taking into account interactions with a hidden sector. In this approach, the smallness of the mass parameters in the NMSSM may be traced back to the original superconformal invariance. This allows to address the \mu-problem and the cosmological domain wall problem in this model, and to implement chaotic inflation in the NMSSM. We discuss the gravitino problem in the NMSSM inflation, as well as the possibility to obtain a broad class of new versions of chaotic inflation in supergravity.