Emergence of conformal properties in Finite Grand Unified Theories via reduction of couplings

Abstract

Zimmermann's Reduction of Couplings (RoC) method is a powerful tool for addressing the problem of the excess of parameters in a field theory, as it yields relations among couplings that are invariant under the renormalization group. Its usefulness becomes particularly evident when constructing predictive supersymmetric GUT models that are free of UV-divergences to all orders. Within this scale-invariant framework, we show that a SUSY model satisfying the conditions of all-loop finiteness exhibits a conformal regime induced by superpotential operators compatible with the RoC. In the soft-breaking sector, the method was shown to lead to a set of scale-invariant relations between the soft couplings and the parameters of the dimensionless sector, among which a sum rule for the scalar masses is particularly notable. These relations closely resemble the typical AMSB relations, while avoiding the tachyonic mass spectrum thanks to the sum rule. Based on this observation, we provide new evidence for a connection between the reduction of parameters in the dimensionful SSB sector and the emergence of an anomaly-mediated (AMSB-like) pattern, under the assumption that the finite Grand Unified Theory is connected to an effective $N=1$, $d=4$ Weyl-invariant SUGRA theory. In this process, we find that an all-order finite model with this property requires a specific form of the K\"ahler potential, whose structure coincides with that studied in no-scale supergravity scenarios.