Superconformal Symmetry, NMSSM, and Inflation

TL;DR

This work develops canonical superconformal supergravity (CSS) as a Jordan-frame framework where chiral and vector multiplets coupled to gravity preserve a local superconformal symmetry, while the pure supergravity sector breaks it to local Poincaré supersymmetry. By embedding scale-invariant NMSSM into CSS and introducing a geometric χ-term (real part of the holomorphic function in scalar-curvature coupling) along with moduli-stabilizing ζ corrections, the authors obtain a simple, global-SUSY-like scalar potential in the Jordan frame and connect nonminimal Higgs-gravity coupling to inflationary dynamics. The paper demonstrates how μ-term generation and domain-wall resolution can emerge from superconformal symmetry breaking, and shows that NMSSM inflation can proceed with controlled stabilization of noninflaton directions, addressing gravitino concerns and enabling a broader class of supergravity inflationary models. These results provide a principled route to combine NMSSM phenomenology with inflation in a unitary, geometrically motivated framework and suggest avenues for constructing chaotic inflation scenarios within supergravity. The approach yields robust inflationary predictions that are largely insensitive to high-energy corrections due to the large χ regime, while maintaining a clear connection between particle physics and cosmology through the underlying superconformal structure.

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 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.

Figures (3)

• Figure 1: Stabilization of the angle $\gamma = \alpha_1+\alpha_2= 0$ near the inflationary trajectory. The infinitely high horseshoe barriers correspond to the singularity of the Kähler geometry. These barriers separate the admissible range of variables from the forbidden part of the landscape (inside the horseshoes), where the argument of the logarithm in the expression for the Kähler potential becomes negative.
• Figure 2: Stabilization of the field $s$ near the inflationary trajectory $s = 0$ for $\zeta > {2|\lambda\rho|\over \lambda^2 h^2} + 0.0327$.
• Figure 3: Contour plots of the potential for the fields $s$ and $h$ during the last 60 e-folds of inflation for $\rho = 0$, $\lambda = 10^{-2}$ and $\xi = 5\times 10^2$, for three different values of $\zeta$. The darker parts correspond to smaller positive density, and the white ovals on the right panel correspond to negative values of the potential. The red arrows show the evolution of the fields during inflation.