Higher-Dimensional Unification with continuous and fuzzy coset spaces as extra dimensions

Gavriil, D.; Manolakos, G.; Orfanidis, Georgios; Zoupanos, George

doi:10.1002/prop.201500022

Cited by 17 publications

(15 citation statements)

References 163 publications

(245 reference statements)

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“…In the context of the construction of noncommutative particle physics models, particularly interesting are the ones that are related to higher dimensions, which are considered to be noncommutative (fuzzy) [67][68][69][70][71][72][73][74][75][76][77][78]. This program has the following advantages: (i) exclusion of the ultraviolet/infrared problematic features; (ii) they are renormalizable, in contrast to all known higher-dimensional theories; and (iii) they give the opportunity to begin with an Abelian gauge group in high dimensions and result with a 4-d theory that is non-Abelian, which means an enhancement in the symmetry of the theory.…”

Section: Introductionmentioning

confidence: 99%

Gauge Theories: From Kaluza–Klein to noncommutative gravity theories

2019

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First, the Coset Space Dimensional Reduction scheme and the best particle physics model so far resulting from it are reviewed. Then, a higher-dimensional theory in which the extra dimensions are fuzzy coset spaces is described and a dimensional reduction to four-dimensional theory is performed. Afterwards, another scheme including fuzzy extra dimensions is presented, but this time the starting theory is four-dimensional while the fuzzy extra dimensions are generated dynamically. The resulting theory and its particle content is discussed. Besides the particle physics models discussed above, gravity theories as gauge theories are reviewed and then, the whole methodology is modified in the case that the background spacetimes are noncommutative. For this reason, specific covariant fuzzy spaces are introduced and, eventually, the program is written for both the 3-d and 4-d cases.

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Section: Introductionmentioning

confidence: 99%

Gauge Theories: From Kaluza–Klein to noncommutative gravity theories

2019

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“…Another very interesting framework which seems to be a natural arena for the description of physics at the Planck scale is the non-commutative geometry [16] - [38]. Regularizing quantum field theories, or even better, building finite ones are the features that render this approach as a promising framework.…”

Section: Introductionmentioning

confidence: 99%

“…A very interesting development in the framework of the non-commutative geometry is the programme in which the extra dimensions of higher -dimensional theories are considered to be non-commutative (fuzzy) [33] - [38]. This programme overcomes the ultraviolet/infrared problematic behaviours of theories defined in non-commutative spaces.…”

Section: Introductionmentioning

confidence: 99%

Non-commutativity in Unified Theories and Gravity

Manolakos

Zoupanos

2018

Springer Proceedings in Mathematics &Amp; Statistics

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First, we briefly review the Coset Space Dimensional Reduction scheme and the results of the best model so far. Then, we present the introduction of fuzzy coset spaces used as extra dimensions and perform a dimensional reduction. In turn, we describe a construction which mimics the results of a reduction, starting from a 4-dimensional theory and we present a successful example of a dynamical generation of fuzzy spheres. Finally, we propose a construction of the 3-d gravity as a gauge theory on specific non-commutative spaces. † To be published in Springer Proc. Math.Stat.

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“…There are several articles on the application of equivariant dimensional reduction method on higher dimensional YM gauge theories as well, for these [27,28,29,30,31,32,33] may be consulted. Other recent interesting articles within this general setting that we do not want to pass without mention include [34,35,36,37,38]. In [34], for instance, an orbifold projection of N = 4 SYM theory have been introduced and extra dimensions which are twisted fuzzy spheres consistent with this orbifolding were found to emerge due to the presence of SSB terms in the model.…”

Section: Introductionmentioning

confidence: 99%

U(3)gauge theory on fuzzy extra dimensions

Kürkçüoğlu

Ünal

2016

Phys. Rev. D

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In this article, we explore the low energy structure of a U (3) gauge theory over spaces with fuzzy sphere(s) as extra dimensions. In particular, we determine the equivariant parametrization of the gauge fields, which transform either invariantly or as vectors under the combined action of SU (2) rotations of the fuzzy spheres and those U (3) gauge transformations generated by SU (2) ⊂ U (3) carrying the spin 1 irreducible representation of SU (2). The cases of a single fuzzy sphere S 2 F and a particular direct sum of concentric fuzzy spheres, S 2 Int F , covering the monopole bundle sectors with windings ±1 are treated in full and the low energy degrees of freedom for the gauge fields are obtained. Employing the parametrizations of the fields in the former case, we determine a low energy action by tracing over the fuzzy sphere and show that the emerging model is abelian Higgs type with U (1) × U (1) gauge symmetry and possess vortex solutions on R 2 , which we discuss in some detail. Generalization of our formulation to the equivariant parametrization of gauge fields in U (n) theories is also briefly addressed.

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Higher-Dimensional Unification with continuous and fuzzy coset spaces as extra dimensions

Cited by 17 publications

References 163 publications

Gauge Theories: From Kaluza–Klein to noncommutative gravity theories

Gauge Theories: From Kaluza–Klein to noncommutative gravity theories

Non-commutativity in Unified Theories and Gravity

U(3)gauge theory on fuzzy extra dimensions

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