Instanton number of noncommutative U(<i>n</i>) gauge theory

Sako, Akifumi

doi:10.1088/1126-6708/2003/04/023

Cited by 21 publications

(31 citation statements)

References 30 publications

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“…The method is to put a cut-off only for the initial and final states, to define the trace operation for finite matrices, i.e. the intermediate states are not restricted by the cut-off, (see [3,4] for details). Using such methods we can estimate the effect of infinite dimension, like the shift operator, by finite size computation.…”

Section: Moyal Plane Case In θ → ∞mentioning

confidence: 99%

“…As another example are the investigations of topological charges. The role of these charges in the noncommutative case is not completely clear yet, however they are topological in commutative space, and thus these charges have some kind of topological nature [3,4,5,6,7,8,9,10,11,12].…”

Section: Introductionmentioning

confidence: 99%

“…For example, the Euler number of a noncommutative torus is independent of the noncommutative parameter θ and it is defined as a topological invariant by the difference of K 0 and K 1 . Another example is the possibility to define the instanton number (the integral of the first Pontrjagin class) as an integer for Moyal space [3,4], and this fact implies that the instanton number has some kind of "topological" nature even for the case that the base manifold is noncommutative space. (Here, we call Moyal space noncommutative Euclidian space whose commutation relations of the coordinates are given by [x µ , x ν ] = iθ µν , where θ µν is an anti-symmetric constant matrix.)…”

Section: Introductionmentioning

confidence: 99%

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Noncommutative Cohomological Field Theories and Topological Aspects of Matrix Models

Sako

2005

Noncommutative Geometry and Physics

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We study topological aspects of matrix models and noncommutative cohomological field theories (N.C.CohFT). N.C.CohFT have symmetry under an arbitrary infinitesimal deformation with noncommutative parameter θ. This fact implies that N.C.CohFT are topologically less sensitive than K-theory, but the classification of manifolds by N.C.CohFT opens the possibility to get a new view point for global characterization of noncommutative manifolds. To investigate the properties of N.C.CohFT, we construct some models whose fixed point loci are given by sets of projection operators. In particular, the partition function on the Moyal plane is calculated by using a matrix model. The moduli space of the matrix model is a union of Grassman manifolds. The partition function of the matrix model is calculated using the Euler number of the Grassman manifold. Identifying the N.C.CohFT with the matrix model, we obtain the partition function of the N.C.CohFT. To check the independence of the noncommutative parameters, we also study the moduli space in the large θ limit and for finite θ, for the case of the Moyal plane. If the partition function of N.C.CohFT is topological in the sense of noncommutative geometry, then this should reveal some relation with K-theory. Therefore we investigate certain models of CohFT and N.C.CohFT from the point of view of K-theory. Our observations give us an analogy between CohFT and N.C.CohFT in connection with K-theory. Furthermore, we verify for the Moyal plane and noncommutative torus cases that our partition functions are invariant under those deformations which do not change the K-theory. Finally, we discuss the noncommutative cohomological Yang-Mills theory.

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Section: Moyal Plane Case In θ → ∞mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Noncommutative Cohomological Field Theories and Topological Aspects of Matrix Models

Sako

2005

Noncommutative Geometry and Physics

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“…In the noncommutative Euclidean space, the instanton number is given by an integer which does not depend on the noncommutative parameter, for the instanton solutions given by ADHM construction [1,2,3,4,5]. Because of these observations, one can ask "Are topological charges unchanged when we deform the space from Euclidean space to noncommutative Euclidean space?".…”

Section: Introductionmentioning

confidence: 99%

Are vortex numbers preserved?

Maeda¹,

Sako²

2008

Journal of Geometry and Physics

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We study noncommutative vortex solutions that minimize the action functional of the Abelian Higgs model in 2-dimensional noncommutative Euclidean space. We first consider vortex solutions which are deformed from solutions defined on commutative Euclidean space to the noncommutative one. We construct solutions whose vortex numbers are unchanged under the noncommutative deformation. Another class of noncommutative vortex solutions via a Fock space representation is also studied.

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“…Either from Corrigan'identity [8][9] [10] or in the operator formalism where the first Pontrjagin class is calculated as a converge series [11][12] [13][14] [15]. In this work we reformulate the ADHM construction of instantons in terms of elements of the A θ (R 4 ) ⊗ A θ (R 4 ) algebra.…”

Section: Introductionmentioning

confidence: 99%

Atiyah-Drinfeld-Hitchin-Manin construction of noncommutativeU(2)k-instantons

Lagraa

2006

Phys. Rev. D

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The basic objects of the ADHM construction are reformulated in terms of elements of the A θ (R 4 ) algebra of the noncommutative R 4 θ space. This new formulation of the ADHM construction makes possible the explicit calculus of the U (2) instanton number which is shown to be the product of a trace of a finite rank projector of the Fock representation space of the algebra A θ (R 4 ) times a noncommutative version of the winding number.

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Instanton number of noncommutative U(n) gauge theory

Cited by 21 publications

References 30 publications

Noncommutative Cohomological Field Theories and Topological Aspects of Matrix Models

Noncommutative Cohomological Field Theories and Topological Aspects of Matrix Models

Are vortex numbers preserved?

Atiyah-Drinfeld-Hitchin-Manin construction of noncommutativeU(2)k-instantons

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