Superconformal Symmetry, NMSSM, and Inflation
  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.
