Superconformal symmetry, NMSSM, and inflation

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 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.

Inflation and String Theory

“…This time only the unprotected field φ−φ receives a mass of order H. Examples of supersymmetric inflation models with these structures can be found in [221,222,239,241,522,523]. Further work on inflation in supergravity includes [480,[524][525][526][527][528][529]. A fundamental limitation of simply assuming a shift symmetry in the low-energy supergravity is that couplings to Planck-mass degrees of freedom 10 A criticism of D-term inflation based on consistency conditions in supergravity can be found in [518].…”

Shift symmetry and Higgs inflation in supergravity with observable gravitational waves

“…It has been shown that HI in the framework of supergravity (SUGRA) can be implemented by imposing [17][18][19][20][21][22][23][24][25][26][27][28][29][30] a convenient shift symmetry on the Kähler potential or invoking [31][32][33][34][35][36][37][38][39][40][41] a logarithmic Kähler potential with a real subdominant kinetic part and a dominant holomorphic (and anti-holomorphic) part, which plays the role of a non-minimal coupling to the Ricci scalar curvature [42][43][44][45][46][47]. Inspired by these efforts, we present here a 'hybrid' scenario, where a conjugate pair of Higgs superfields is involved in the logarithmic part of the Kähler potential K, which respects a shift symmetry with a tiny violation -cf.…”

Scale factor self-dual cosmological models

“…We begin with the encouraging observation that by a simple change of the field variable φ 2 = ΦΦ = 6 tanh 2 (δσ) (with κ 2 = 2) our self-dual models (4.4) are transformed into SU(1, 1)/U(1) Kähler sigma models, 6 with gauge fixed U(1) symmetry Φ =Φ = φ and minimally coupled to Einstein gravity. Indeed such an embedding into N = 1 supergravity with one chiral matter supermultiplet is quite natural and expected due to its well known role in the construction of both quintessence [15-17, 19, 20] and inflationary models [9][10][11][12][13]34]. The new feature, however, consists in a very special relation between the Kähler potential K(Φ,Φ) and the superpotential |Z| = W(φ) = e K 2 |W |,…”

“…It is worthwhile to also mention that the inflationary α-attractors [5,6], obtained within the superconformal supergravity approach [12,13], for a special choice of the inflaton potential:…”

“…The increasing precision of the recent astrophysical data [1,2] allows to further select a restricted number of favored shapes of the corresponding potentials [3], thus providing important hints in the search of dynamical symmetry principles governing the universe evolution [4][5][6][7][8]. At extremely high energies, where no preferred scales exist, the conformal or Weyl symmetries completely determine the corresponding effective gravity-matter actions [9][10][11][12][13]. The description of lower densities and large scales phenomena, however, requires spontaneous or explicit breaking of the scale invariance [4-6, 8, 14].…”