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 Poincaré 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 µ-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.

We study the critical points of the black hole scalar potential V BH in N = 2, d = 4 supergravity coupled to n V vector multiplets, in an asymptotically flat extremal black hole background described by a 2 (n V + 1)-dimensional dyonic charge vector and (complex) scalar fields which are coordinates of a special Kähler manifold.For the case of homogeneous symmetric spaces, we find three general classes of regular attractor solutions with non-vanishing Bekenstein-Hawking entropy. They correspond to three (inequivalent) classes of orbits of the charge vector, which is in a 2 (n V + 1)-dimensional representation R V of the U-duality group. Such orbits are non-degenerate, namely they have non-vanishing quartic invariant (for rank-3 spaces). Other than the 1 2 -BPS one, there are two other distinct non-BPS classes of charge orbits, one of which has vanishing central charge.The three species of solutions to the N = 2 extremal black hole attractor equations give rise to different mass spectra of the scalar fluctuations, whose pattern can be inferred by using invariance properties of the critical points of V BH and some group theoretical considerations on homogeneous symmetric special Kähler geometry.

We present a complete explicit N = 1, d = 4 supergravity action in an arbitrary Jordan frame with non-minimal scalar-curvature coupling of the form Φ(z,z) R. The action is derived by suitably gauge-fixing the superconformal action. The theory has a modified Kähler geometry, and it exhibits a significant dependence on the frame function Φ(z,z) and its derivatives over scalars, in the bosonic as well as in the fermionic part of the action. Under certain simple conditions, the scalar kinetic terms in the Jordan frame have a canonical form.We consider an embedding of the Next-to-Minimal Supersymmetric Standard Model (NMSSM) gauge theory into supergravity, clarifying the Higgs inflation model recently proposed by Einhorn and Jones. We find that the conditions for canonical kinetic terms are satisfied for the NMSSM scalars in the Jordan frame, which leads to a simple action. However, we find that the gauge singlet field experiences a strong tachyonic instability during inflation in this model. Thus, a modification of the model is required to support the Higgs-type inflation.

Abstract:We identify the space of symplectic deformations of maximal gauged supergravity theories. Coordinates of such space parametrize inequivalent supergravity models with the same gauge group. We apply our procedure to the SO(8) gauging, extending recent analyses. We also study other interesting cases, including Cremmer-Scherk-Schwarz models and gaugings of groups contained in SL(8, R) and in SU * (8).