Unified Gauge Theories and Reduction of Couplings: from Finiteness to Fuzzy Extra Dimensions

TL;DR

This paper explores finite supersymmetric grand unified theories with reduced couplings, predicts particle masses, and investigates gauge theories in higher dimensions with fuzzy extra dimensions, revealing novel symmetry breaking and renormalizability features.

Contribution

It combines the study of finite unified theories with higher-dimensional gauge theories on fuzzy spaces, introducing a new perspective on symmetry breaking and renormalizability.

Findings

Predicted top quark and Higgs boson masses with high accuracy

Demonstrated emergence of non-Abelian gauge theories from Abelian theories in higher dimensions

Showed spontaneous symmetry breaking occurs in extra dimensions leading to fuzzy spheres

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 such FUTs. Next we consider gauge theories defined in higher dimensions, where the extra dimensions form a fuzzy space (a finite matrix manifold). We reinterpret these gauge theories as four-dimensional theories with Kaluza-Klein modes. We then perform a generalized a la Forgacs-Manton dimensional reduction. We emphasize some striking features emerging such as (i)the appearance of non-Abelian gauge theories in four dimensions starting from an Abelian gauge theory in higher dimensions, (ii) the fact that the spontaneous symmetry breaking of the theory takes place entirely in the extra dimensions and (iii) the renormalizability of the theory both in higher as well as in four dimensions. Then reversing the above approach we present a renormalizable four dimensional SU(N) gauge theory with a suitable multiplet of scalar fields, which via spontaneous symmetry breaking dynamically develops extra dimensions in the form of a fuzzy sphere $S^2_N$.