10,934 research outputs found

    Fuzzy Extra Dimensions: Dimensional Reduction, Dynamical Generation and Renormalizability

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    We examine gauge theories defined in higher dimensions where theextra dimensions form a fuzzy (finite matrix) manifold. First we reinterpret these gauge theories as four-dimensional theories with Kaluza-Klein modes and then we perform a generalized \`a la Forgacs-Manton dimensional reduction. We emphasize some striking features emerging in the later case 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. We explicitly find the tower of massive Kaluza-Klein modes consistent with an interpretation as gauge theory on M4×S2M^4 \times S^2, the scalars being interpreted as gauge fields on S2S^2. Depending on the parameters of the model the low-energy gauge group can be of the form SU(n1)×SU(n2)×U(1)SU(n_1) \times SU(n_2) \times U(1).Comment: 18 pages, Based on invited talks presented at various conferences, Minor corrections, Acknowledgements adde

    New Fuzzy Extra Dimensions from SU(N)SU({\cal N}) Gauge Theories

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    We start with an SU(N)SU(\cal {N}) Yang-Mills theory on a manifold M{\cal M}, suitably coupled to two distinct set of scalar fields in the adjoint representation of SU(N)SU({\cal N}), which are forming a doublet and a triplet, respectively under a global SU(2)SU(2) symmetry. We show that a direct sum of fuzzy spheres SF2Int:=SF2()SF2()SF2(+12)SF2(12)S_F^{2 \, Int} := S_F^2(\ell) \oplus S_F^2 (\ell) \oplus S_F^2 \left ( \ell + \frac{1}{2} \right ) \oplus S_F^2 \left ( \ell - \frac{1}{2} \right ) emerges as the vacuum solution after the spontaneous breaking of the gauge symmetry and lay the way for us to interpret the spontaneously broken model as a U(n)U(n) gauge theory over M×SF2Int{\cal M} \times S_F^{2 \, Int}. Focusing on a U(2)U(2) gauge theory we present complete parameterizations of the SU(2)SU(2)-equivariant, scalar, spinor and vector fields characterizing the effective low energy features of this model. Next, we direct our attention to the monopole bundles SF2±:=SF2()SF2(±12)S_F^{2 \, \pm} := S_F^2 (\ell) \oplus S_F^2 \left ( \ell \pm \frac{1}{2} \right ) over SF2()S_F^2 (\ell) with winding numbers ±1\pm 1, which naturally come forth through certain projections of SF2IntS_F^{2 \, Int}, and discuss the low energy behaviour of the U(2)U(2) gauge theory over M×SF2±{\cal M} \times S_F^{2 \, \pm}. We study models with kk-component multiplet of the global SU(2)SU(2), give their vacuum solutions and obtain a class of winding number ±(k1)\pm (k-1) monopole bundles SF2,±(k1)S_F^{2 \,, \pm (k-1)} as certain projections of these vacuum solutions. We make the observation that SF2IntS_F^{2 \, Int} is indeed the bosonic part of the N=2N=2 fuzzy supersphere with OSP(2,2)OSP(2,2) supersymmetry and construct the generators of the osp(2,2)osp(2,2) Lie superalgebra in two of its irreducible representations using the matrix content of the vacuum solution SF2IntS_F^{2 \, Int}. Finally, we show that our vacuum solutions are stable by demonstrating that they form mixed states with non-zero von Neumann entropy.Comment: 27+1 pages, revised version, added references and corrected typo

    Matrix Models in Homogeneous Spaces

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    We investigate non-commutative gauge theories in homogeneous spaces G/H. We construct such theories by adding cubic terms to IIB matrix model which contain the structure constants of G. The isometry of a homogeneous space, G must be a subgroup of SO(10) in our construction. We investigate CP^2=SU(3)/U(2) case in detail which gives rise to 4 dimensional non-commutative gauge theory. We show that non-commutative gauge theory on R^4 can be realized in the large N limit by letting the action approach IIB matrix model in a definite way. We discuss possible relevances of these theories to the large N limit of IIB matrix model.Comment: 21 pages, sign errors in one loop effective action are correcte

    OSp(4|2) Superconformal Mechanics

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    A new superconformal mechanics with OSp(4|2) symmetry is obtained by gauging the U(1) isometry of a superfield model. It is the one-particle case of the new N=4 super Calogero model recently proposed in arXiv:0812.4276 [hep-th]. Classical and quantum generators of the osp(4|2) superalgebra are constructed on physical states. As opposed to other realizations of N=4 superconformal algebras, all supertranslation generators are linear in the odd variables, similarly to the N=2 case. The bosonic sector of the component action is standard one-particle (dilatonic) conformal mechanics accompanied by an SU(2)/U(1) Wess-Zumino term, which gives rise to a fuzzy sphere upon quantization. The strength of the conformal potential is quantized.Comment: 1+20 pages, v2: typos fixed, for publication in JHE

    Quantum Entropy for the Fuzzy Sphere and its Monopoles

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    Using generalized bosons, we construct the fuzzy sphere SF2S_F^2 and monopoles on SF2S_F^2 in a reducible representation of SU(2)SU(2). The corresponding quantum states are naturally obtained using the GNS-construction. We show that there is an emergent non-abelian unitary gauge symmetry which is in the commutant of the algebra of observables. The quantum states are necessarily mixed and have non-vanishing von Neumann entropy, which increases monotonically under a bistochastic Markov map. The maximum value of the entropy has a simple relation to the degeneracy of the irreps that constitute the reducible representation that underlies the fuzzy sphere.Comment: 21 pages, typos correcte
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