Dynamical generation of gauge groups in the massive Yang-Mills–Chern-Simons matrix model

Azuma, Takehiro; Bal, Subrata; Nishimura, Jun

doi:10.1103/physrevd.72.066005

Cited by 33 publications

(54 citation statements)

References 30 publications

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“…In particular, previous studies based on actions for fuzzy gauge theory different from ours generically only gave results corresponding to U(1) or U(∞) gauge groups, see e.g. [10][11][12] and references therein. The dynamical generation of a nontrivial index on noncommutative spaces has also been observed in [13,14] for different models.…”

Section: Introductionmentioning

confidence: 99%

Dynamical generation of fuzzy extra dimensions, dimensional reduction and symmetry breaking

Aschieri

Grammatikopoulos

Steinacker

et al. 2006

J. High Energy Phys.

222

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We present a renormalizable 4-dimensional SU(N ) gauge theory with a suitable multiplet of scalar fields, which dynamically develops extra dimensions in the form of a fuzzy sphere S 2 N . We explicitly find the tower of massive KaluzaKlein modes consistent with an interpretation as gauge theory on M 4 × S 2 , the scalars being interpreted as gauge fields on S 2 . The gauge group is broken dynamically, and the low-energy content of the model is determined. Depending on the parameters of the model the low-energy gauge group can be SU(n), or broken further to SU(n 1 ) × SU(n 2 ) × U(1), with mass scale determined by the size of the extra dimension.

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Section: Introductionmentioning

confidence: 99%

Dynamical generation of fuzzy extra dimensions, dimensional reduction and symmetry breaking

Aschieri

Grammatikopoulos

Steinacker

et al. 2006

J. High Energy Phys.

222

View full text Add to dashboard Cite

show abstract

“…In particular, previous studies based on actions for fuzzy gauge theory different from ours generically only gave results corresponding to U (1) or U (∞) gauge groups, see e.g. [77,78,79] and references therein. The dynamical generation of a nontrivial index on noncommutative spaces has also been observed in [80,81] for different models.…”

Section: Emergence Of Extra Dimensions and The Fuzzy Spherementioning

confidence: 99%

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

Mondragón

Zoupanos

2008

SIGMA

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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 . We explicitly find the tower of massive Kaluza-Klein modes consistent with an interpretation as gauge theory on M 4 × 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 ) × SU (n 2 ) × 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.

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“…In the computation of the partition function for off-diagonal fluctuations, we should diag- † Stability of fuzzy spheres is discussed in the IIB matrix model with Chern-Simons term [30] and mass term [31].…”

Section: Free Energy Of Fuzzy Membrane Interactionmentioning

confidence: 99%

Thermodynamic behavior of fuzzy membranes in pp-wave matrix model

Shin

Yoshida

2005

Physics Letters B

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We discuss a two-body interaction of membrane fuzzy spheres in a pp-wave matrix model at finite temperature by considering a fuzzy sphere rotates with a constant radius r around the other one sitting at the origin in the SO(6) symmetric space. This system of two fuzzy spheres is supersymmetric at zero temperature and there is no interaction between them. Once the system is coupled to the heat bath, supersymmetries are completely broken and non-trivial interaction appears. We numerically show that the potential between fuzzy spheres is attractive and so the rotating fuzzy sphere tends to fall into the origin. The analytic formula of the free energy is also evaluated in the large N limit. It is well approximated by a polylog-function.

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Dynamical generation of gauge groups in the massive Yang-Mills–Chern-Simons matrix model

Cited by 33 publications

References 30 publications

Dynamical generation of fuzzy extra dimensions, dimensional reduction and symmetry breaking

Dynamical generation of fuzzy extra dimensions, dimensional reduction and symmetry breaking

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

Thermodynamic behavior of fuzzy membranes in pp-wave matrix model

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