Noncommutative solitons on Kahler manifolds

Spradlin, Marcus; Volovich, Anastasia

doi:10.1088/1126-6708/2002/03/011

Cited by 12 publications

(19 citation statements)

References 62 publications

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“…Berezin's geometric quantization [10,11] of a Kähler space M describes the quantum mechanics of a particle whose phase space is M . In this paper we will be interested in the special case when M = CY 3 is a Calabi-Yau threefold.…”

Section: Brief Review Of Geometric Quantization and The Star Productmentioning

confidence: 99%

D0-branes in black hole attractors

Gaiotto

Simons

Strominger

et al. 2006

J. High Energy Phys.

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Configurations of N probe D0-branes in a Calabi-Yau black hole are studied. A large degeneracy of near-horizon bound states are found which can be described as lowest Landau levels tiling the horizon of the black hole. These states preserve some of the enhanced supersymmetry of the near-horizon AdS 2 × S 2 × CY 3 attractor geometry, but not of the full asymptotically flat solution. Supersymmetric non-abelian configurations are constructed which, via the Myers effect, develop charges associated with higher-dimensional branes wrapping CY 3 cycles. An SU (1, 1|2) superconformal quantum mechanics describing D0-branes in the attractor geometry is explicitly constructed.

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Section: Brief Review Of Geometric Quantization and The Star Productmentioning

confidence: 99%

D0-branes in black hole attractors

Gaiotto

Simons

Strominger

et al. 2006

J. High Energy Phys.

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“…Although these expectations have not materialized up to now, noncommutative field theory and its quantum mechanical mini-superspace have led to many new and interesting results. In particular, in the context of string theory there has been a lot of interest in studying solitonic solutions of noncommutative field theory [11,19]. Also motivated by that work, but in a somewhat different direction, coherent structures in the form of noncommutative solitons and vortices were studied by the authors in a recent collaboration [14].…”

Section: Introductionmentioning

confidence: 99%

On deformed quantum mechanical schemes and ★-value equations based on the space-space noncommutative Heisenberg-Weyl group

Juárez

Rosenbaum

2010

J. Phys. Math.

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We investigate the Weyl-Wigner-Gröenewold-Moyal, the Stratonovich and the Berezin group quantization schemes for the space-space noncommutative Heisenberg-Weyl group. We show that the ⋆-product for the deformed algebra of Weyl functions for the first scheme is different than that for the other two, even though their respective quantum mechanics' are equivalent as far as expectation values are concerned, provided that some additional criteria are imposed on the implementation of this process. We also show that it is the ⋆-product associated with the Stratonovich and the Berezin formalisms that correctly gives the Weyl symbol of a product of operators in terms of the deformed product of their corresponding Weyl symbols. To conclude, we derive the stronger ⋆-valued equations for the 3 quantization schemes considered and discuss the criteria that are also needed for them to exist.

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“…The proof is based on using energy estimates which indeed show that the energy of two infinitely separated solitons is greater than that of two overlapping ones. Various aspects of the theory of solitons in noncommutative scalar field theories are discussed in [6,7,8,9,10,11,12,13].…”

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confidence: 99%