Dynamical generation of a nontrivial index on the fuzzy 2-sphere

222

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.

“…[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: 93%

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

Aschieri

Grammatikopoulos

Steinacker

et al. 2006

222

“…[27][28][29][30][31][32][33][34][35][36][37][38][39]. This provides a matrix description of the so-called Myers effect in string theory [40].…”

Section: Introductionmentioning

confidence: 99%

“…Yet another motivation is to use the fuzzy sphere (or its generalization [46,47]) as a regularization scheme alternative to the lattice regularization [48]. Unlike the lattice, fuzzy spheres preserve the continuous symmetries of the space-time considered, and hence it is expected to ameliorate the well-known problem concerning chiral symmetry [36,[49][50][51][52][53][54][55][56][57][58][59][60][61][62][63] and supersymmetry. A challenge in this direction is to remove the effects of noncommutativity of the space-time in the "continuum limit".…”

Section: Introductionmentioning

confidence: 99%

Impact of supersymmetry on the nonperturbative dynamics of fuzzy spheres

Anagnostopoulos

Azuma

Nagao

et al. 2005

Self Cite

We study a 4d supersymmetric matrix model with a cubic term, which incorporates fuzzy spheres as classical solutions, using Monte Carlo simulations and perturbative calculations. The fuzzy sphere in the supersymmetric model turns out to be always stable if the large-N limit is taken in such a way that various correlation functions scale. This is in striking contrast to analogous bosonic models, where the fuzzy sphere decays into the pure Yang-Mills vacuum due to quantum effects when the coefficient of the cubic term becomes smaller than a critical value. We also find that the power-law tail of the eigenvalue distribution, which exists in the supersymmetric model without the cubic term, disappears in the presence of the fuzzy sphere in the large-N limit. Coincident fuzzy spheres turn out to be unstable, which implies that the dynamically generated gauge group is U(1).

“…First we consider the possibility that NC geometry is realized in the extra dimensions [13,14]. There is a well-known scenario in string theory that the number of generations, for instance, is determined by the index in the extra dimensions.…”

Section: Summary and Discussionmentioning

confidence: 99%

Dominance of a single topological sector in gauge theory on non-commutative geometry

Aoki

Nishimura

Susaki

2009

Self Cite

We demonstrate a striking effect of non-commutative (NC) geometry on topological properties of gauge theory by Monte Carlo simulations. We study 2d U(1) NC gauge theory for various boundary conditions using a new finite-matrix formulation proposed recently. We find that a single topological sector dictated by the boundary condition dominates in the continuum limit. This is in sharp contrast to the results in commutative space-time based on lattice gauge theory, where all topological sectors appear with certain weights in the continuum limit. We discuss possible implications of this effect in the context of string theory compactifications and in field theory contexts.