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22
Effective actions of matrix models on homogeneous spaces
 Nucl. Phys. B
"... We evaluate the effective actions of supersymmetric matrix models on fuzzy S2 × S2 up to the two loop level. Remarkably it turns out to be a consistent solution of IIB matrix model. Based on the power counting and SUSY cancellation arguments, we can identify the ’t Hooft coupling and large N scaling ..."
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Cited by 31 (2 self)
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We evaluate the effective actions of supersymmetric matrix models on fuzzy S2 × S2 up to the two loop level. Remarkably it turns out to be a consistent solution of IIB matrix model. Based on the power counting and SUSY cancellation arguments, we can identify the ’t Hooft coupling and large N scaling behavior of the effective actions to all orders. In the large N limit, the quantum corrections survive except in 2 dimensional limits. They are O(N) and O(N 4 3) for 4 and 6 dimensional spaces respectively. We argue that quantum effects single out 4 dimensionality of spacetime.
Nonabelian gauge field and dual description of fuzzy sphere
 JHEP 0404 (2004) 058 [arXiv:hepth/0402044
"... In matrix models, higher dimensional Dbranes are obtained by imposing a noncommutative relation to coordinates of lower dimensional Dbranes. On the other hand, a dual description of this noncommutative space is provided by higher dimensional Dbranes with gauge fields. Fuzzy spheres can appear as ..."
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Cited by 19 (1 self)
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In matrix models, higher dimensional Dbranes are obtained by imposing a noncommutative relation to coordinates of lower dimensional Dbranes. On the other hand, a dual description of this noncommutative space is provided by higher dimensional Dbranes with gauge fields. Fuzzy spheres can appear as a configuration of lower dimensional Dbranes in a constant RR field strength background. In this paper, we consider a dual description of higher dimensional fuzzy spheres by introducing nonabelian gauge fields on higher dimensional spherical Dbranes. By using the BornInfeld action, we show that a fuzzy 2ksphere and spherical D2kbranes with a nonabelian gauge field whose Chern character is nontrivial are the same objects when n is large. We discuss a relationship between the noncommutative geometry and nonabelian gauge fields. Nonabelian gauge fields are represented by noncommutative matrices including the coordinate dependence. A similarity to the quantum Hall system is also studied. 1 1
Fuzzy supersphere and supermonopole
 Nucl. Phys. B709
"... It is wellknown that coordinates of a charged particle in the presence of a monopole background become noncommutative. In this paper, we study the motion of a charged particle moving on a supersphere in the presence of a supermonopole. We construct a supermonopole by using a supersymmetric extensio ..."
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Cited by 7 (1 self)
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It is wellknown that coordinates of a charged particle in the presence of a monopole background become noncommutative. In this paper, we study the motion of a charged particle moving on a supersphere in the presence of a supermonopole. We construct a supermonopole by using a supersymmetric extension of the first Hopf map. We investigate algebras of angular momentum operators and supersymmetry generators in the supermonopole background. It is shown that coordinates of the particle are described by fuzzy supersphere in the lowest Landau level. We find that there exist two kinds of degenerate wavefunctions due to the supersymmetry. Ground state wavefunctions are given by the Hopf spinor and we discuss their several properties. 1 1
Correlators of Matrix Models on Homogeneous Spaces
, 2004
"... We investigate the correlators of TrAµAν in matrix models on homogeneous spaces: S 2 and S 2 × S 2. Their expectation value is a good order parameter to measure the geometry of the space on which noncommutative gauge theory is realized. They also serve as the Wilson lines which carry the minimum mo ..."
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Cited by 7 (0 self)
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We investigate the correlators of TrAµAν in matrix models on homogeneous spaces: S 2 and S 2 × S 2. Their expectation value is a good order parameter to measure the geometry of the space on which noncommutative gauge theory is realized. They also serve as the Wilson lines which carry the minimum momentum. We develop an efficient procedure to calculate them through 1PI diagrams. We determine the large N scaling behavior of the correlators. The order parameter shows that fuzzy S 2 × S 2 acquires a 4 dimensional fractal structure in contrast to fuzzy S 2. We also find that the two point functions exhibit logarithmic scaling violations.
SpinHall effect with quantum group symmetry
 Lett. Math. Phys
, 2006
"... We construct a model of spinHall effect on the noncommutative sphere S 4 θ with isospin degrees of freedom (coming from a noncommutative instanton) and invariance under a quantum group SOθ(5). The corresponding representation theory allows to explicitly diagonalize the Hamiltonian and construct the ..."
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Cited by 7 (3 self)
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We construct a model of spinHall effect on the noncommutative sphere S 4 θ with isospin degrees of freedom (coming from a noncommutative instanton) and invariance under a quantum group SOθ(5). The corresponding representation theory allows to explicitly diagonalize the Hamiltonian and construct the ground state; there are both integer and fractional excitations. Similar models exist on higher dimensional spheres S N Θ and projective spaces CPN Θ.
DIASSTP0309 Fuzzy Complex Quadrics and Spheres
, 2008
"... A matrix algebra is constructed which consists of the necessary degrees of freedom for a finite approximation to the algebra of functions on the family of orthogonal Grassmannians of real dimension 2N, known as complex quadrics. These matrix algebras contain the relevant degrees of freedom for descr ..."
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Cited by 6 (1 self)
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A matrix algebra is constructed which consists of the necessary degrees of freedom for a finite approximation to the algebra of functions on the family of orthogonal Grassmannians of real dimension 2N, known as complex quadrics. These matrix algebras contain the relevant degrees of freedom for describing truncations of harmonic expansions of functions on Nspheres. An InönüWigner contraction of the quadric gives the cotangent bundle to the commutative sphere in the continuum limit. It is shown how the degrees of freedom for the sphere can be projected out of a finite dimensional functional integral, using secondorder Casimirs, giving a welldefined procedure for construction functional integrals over fuzzy spheres of any dimension.
Oscillator potential for the fourdimensional Hall effect
, 2005
"... We suggest the exactly solvable model of oscillator on the fourdimensional sphere interacting with the SU(2) Yang monopole. We show, that the properties of the model essentially depend on the monopole charge. ..."
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Cited by 2 (1 self)
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We suggest the exactly solvable model of oscillator on the fourdimensional sphere interacting with the SU(2) Yang monopole. We show, that the properties of the model essentially depend on the monopole charge.
KEKTH821 Noncommutative Gauge Theory on Fuzzy FourSphere and Matrix Model
, 2002
"... We study a noncommutative gauge theory on a fuzzy foursphere. The idea is to use a matrix model with a fifthrank ChernSimons term and to expand matrices around the fuzzy foursphere which corresponds to a classical solution of this model. We need extra degrees of freedom since algebra of coordina ..."
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We study a noncommutative gauge theory on a fuzzy foursphere. The idea is to use a matrix model with a fifthrank ChernSimons term and to expand matrices around the fuzzy foursphere which corresponds to a classical solution of this model. We need extra degrees of freedom since algebra of coordinates does not close on the fuzzy foursphere. In such a construction, a fuzzy two sphere is added at each point on the fuzzy foursphere as extra degrees of freedom. It is interesting that fields on the fuzzy foursphere have higher spins due to the extra degrees of freedom. We also consider a theory around the north pole and take a flat space limit. A noncommutative gauge theory on fourdimensional plane, which has Heisenberg type noncommutativity, is considered. 1 1