10,934 research outputs found
Fuzzy Extra Dimensions: Dimensional Reduction, Dynamical Generation and Renormalizability
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 , the scalars being interpreted as gauge fields on . Depending
on the parameters of the model the low-energy gauge group can be of the form
.Comment: 18 pages, Based on invited talks presented at various conferences,
Minor corrections, Acknowledgements adde
New Fuzzy Extra Dimensions from Gauge Theories
We start with an Yang-Mills theory on a manifold ,
suitably coupled to two distinct set of scalar fields in the adjoint
representation of , which are forming a doublet and a triplet,
respectively under a global symmetry. We show that a direct sum of
fuzzy spheres 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 gauge theory over . Focusing
on a gauge theory we present complete parameterizations of the
-equivariant, scalar, spinor and vector fields characterizing the
effective low energy features of this model. Next, we direct our attention to
the monopole bundles over with winding numbers ,
which naturally come forth through certain projections of , and
discuss the low energy behaviour of the gauge theory over . We study models with -component multiplet of the
global , give their vacuum solutions and obtain a class of winding
number monopole bundles as certain
projections of these vacuum solutions. We make the observation that is indeed the bosonic part of the fuzzy supersphere with
supersymmetry and construct the generators of the Lie superalgebra
in two of its irreducible representations using the matrix content of the
vacuum solution . 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
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
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
Using generalized bosons, we construct the fuzzy sphere and monopoles
on in a reducible representation of . 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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