Unified gauge theories and reduction of couplings: From finiteness to fuzzy extra dimensions

Mondragon, M; Zoupanos, G

dc.contributor.author	Mondragon, M	en
dc.contributor.author	Zoupanos, G	en
dc.date.accessioned	2014-03-01T01:29:27Z
dc.date.available	2014-03-01T01:29:27Z
dc.date.issued	2008	en
dc.identifier.issn	1815-0659	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/19264
dc.subject	Finiteness	en
dc.subject	Fuzzy sphere	en
dc.subject	Gauge theories	en
dc.subject	Higher dimensions	en
dc.subject	Non-commutative gauge theories	en
dc.subject	Renormalizability	en
dc.subject	Unification	en
dc.subject.other	SOFT SUPERSYMMETRY-BREAKING	en
dc.subject.other	NONCOMMUTATIVE STANDARD MODEL	en
dc.subject.other	PROBE WMAP OBSERVATIONS	en
dc.subject.other	QUANTUM-FIELD THEORIES	en
dc.subject.other	EVEN HIGGS BOSONS	en
dc.subject.other	FERMION MASSES	en
dc.subject.other	SYMMETRY-BREAKING	en
dc.subject.other	BETA-FUNCTIONS	en
dc.subject.other	COSET SPACES	en
dc.subject.other	MSSM	en
dc.title	Unified gauge theories and reduction of couplings: From finiteness to fuzzy extra dimensions	en
heal.type	journalArticle	en
heal.identifier.primary	10.3842/SIGMA.2008.026	en
heal.identifier.secondary	http://dx.doi.org/10.3842/SIGMA.2008.026	en
heal.identifier.secondary	026	en
heal.language	English	en
heal.publicationDate	2008	en
heal.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-N(2). We explicitly find the tower of massive Kaluza-Klein modes consistent with an interpretation as gauge theory on M-4 x S-2, the scalars being interpreted as gauge fields on S-2. Depending on the parameters of the model the low-energy gauge group can be SU(n), or broken further to SU(n(1)) x SU(n(2)) x U(1). Therefore the second picture justifies the first one in a renormalizable framework but in addition has the potential to reveal new aspects of the theory.	en
heal.publisher	NATL ACAD SCI UKRAINE, INST MATH	en
heal.journalName	Symmetry, Integrability and Geometry: Methods and Applications	en
dc.identifier.doi	10.3842/SIGMA.2008.026	en
dc.identifier.isi	ISI:000267267800026	en
dc.identifier.volume	4	en