Finite Unification: Theory and Predictions

TL;DR

This paper discusses all-loop finite supersymmetric GUTs with reduced couplings, presenting models based on SU(5) and SU(3)^3 gauge groups, and highlights their predictive power, including Higgs mass predictions testable at the LHC.

Contribution

It introduces new finite GUT models with exact RGI relations, extending finiteness to soft supersymmetry breaking sectors, and provides phenomenological predictions.

Findings

FUT models based on SU(5) and SU(3)^3 gauge groups.

Predictions of Higgs mass testable at the LHC.

All-loop finiteness achieved through RGI relations.

Abstract

All-loop Finite Unified Theories (FUTs) are very interesting N=1 supersymmetric Grand Unified Theories (GUTs) which not only realise an old field theoretic dream but also have a remarkable predictive power due to the required reduction of couplings. The reduction of the dimensionless couplings in N=1 GUTs is achieved by searching for renormalization group invariant (RGI) relations among them holding beyond the unification scale. Finiteness results from the fact that there exist RGI relations among dimensionless couplings that guarantee the vanishing of all beta-functions in certain N=1 GUTs even to all orders. Furthermore developments in the soft supersymmetry breaking sector of N=1 GUTs and FUTs lead to exact RGI relations, i.e. reduction of couplings, in this dimensionful sector of the theory too. Based on the above theoretical framework phenomenologically consistent FUTS have been constructed. Here we present FUT models based on the SU(5) and SU(3)^3 gauge groups and their predictions. Of particular interest is the Higgs mass prediction of one of the models which is expected to be tested at the LHC.