Unified Theories: From Finiteness to Fuzzy Extra Dimensions

Abstract

Finite Unified Theories (FUTs) are N = 1 supersymmetric Grand Unified Theories, which can be made all-loop finite, both in the dimensionless (gauge and Yukawa couplings) and dimensionful (soft supersymmetry breaking terms) sectors. This remarkable property, based on the reduction of couplings at the quantum level, provides a drastic reduction in the number of free parameters, which in turn leads to an accurate prediction of the top quark mass in the dimensionless sector, and predictions for the Higgs boson mass and the supersymmetric spectrum in the dimensionful sector. Here we examine the predictions of two FUTs taking into account all theoretical andexperimental constraints. Unified theories defined in more than four dimensions provide after dimensional reduction in four dimensions a further unification of the gauge, Yukawa and Higgs sectors as well as of the soft supersymmetry breaking sector in the case of supersymmetric theories. Furthermore, if the extra dimensions are fuzzy instead of continuous, the theories become renormalizable. Due to lack of space we cannot review the last two subjects here and we suggest consultation of the original papers.