Dimensional Reduction over Fuzzy Coset Spaces

We give a non-perturbative definition of U(n) gauge theory on fuzzy CP 2 as a multi-matrix model. The degrees of freedom are 8 hermitian matrices of finite size, 4 of which are tangential gauge fields and 4 are auxiliary variables. The model depends on a noncommutativity parameter 1 N , and reduces to the usual U(n) Yang-Mills action on the 4-dimensional classical CP 2 in the limit N → ∞. We explicitly find the monopole solutions, and also certain U(2) instanton solutions for finite N. The quantization of the model is defined in terms of a path integral, which is manifestly finite. An alternative formulation with constraints is also given, and a scaling limit as R 4 θ is discussed.

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“…We extend its action to tensor fields with indices in su(3) in the natural way (cp. [26]), in particular…”

Section: Field Strength Action and Chern Classmentioning

confidence: 99%

Finite gauge theory on fuzzy CP2

2005

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“…up to a gauge transformation, where X (N ) a denote the generator of the N-dimensional irrep of SU (2). This can be viewed as a special case of (15) below, consisting of n copies of the irrep (N) of SU (2).…”

Section: The Minimum Of the Potentialmentioning

confidence: 99%

“…This can be viewed as a special case of (15) below, consisting of n copies of the irrep (N) of SU (2).…”

Section: The Minimum Of the Potentialmentioning

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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“…It has been applied in a variety of contexts in [9,10] when the internal coset space is the projective line CP 1 . Dimensional reduction over the fuzzy sphere CP 1 F is also considered in [10,11]. In this paper we extend the analysis of the vacuum states of such quiver gauge theories performed in [10] to an example with non-abelian holonomy, the projective plane CP 2 .…”

Section: Introductionmentioning

confidence: 99%

Dimensional reduction and vacuum structure of quiver gauge theory

Dolan¹,

Szabo²

2009

J. High Energy Phys.

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We describe the structure of the vacuum states of quiver gauge theories obtained via dimensional reduction over homogeneous spaces, in the explicit example of SU(3)-equivariant dimensional reduction of Yang-Mills-Dirac theory on manifolds of the form M × CP 2 . We pay particular attention to the role of topology of background gauge fields on the internal coset spaces, in this case U(1) magnetic monopoles and SU(2) instantons on CP 2 . The reduction of Yang-Mills theory induces a quiver gauge theory involving coupled Yang-Mills-Higgs systems on M with a Higgs potential leading to dynamical symmetry breaking. The criterion for a ground state of the Higgs potential can be written as the vanishing of a non-abelian Yang-Mills flux on the quiver diagram, regarded as a lattice with group elements attached to the links. The reduction of SU(3)-symmetric fermions yields Dirac fermions on M transforming under the low-energy gauge group with Yukawa couplings. The fermionic zero modes on CP 2 yield exactly massless chiral fermions on M , though there is a unique choice of spin c structure on CP 2 for which some of the zero modes can acquire masses through Yukawa interactions. We work out the spontaneous symmetry breaking patterns and determine the complete physical particle spectrum in a number of explicit examples, some of which possess quantum number assignments qualitatively analogous to the manner in which vector bosons, quarks and leptons acquire masses in the standard model.

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Dimensional Reduction over Fuzzy Coset Spaces

Cited by 64 publications

References 74 publications

Finite gauge theory on fuzzy CP2

Finite gauge theory on fuzzy CP2

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

Dimensional reduction and vacuum structure of quiver gauge theory

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