The CP(n) model on noncommutative plane

Lee, Bum-Hoon; Lee, Kimyeong; Yang, Hyun Seok

doi:10.1016/s0370-2693(01)00006-5

Cited by 44 publications

(68 citation statements)

References 53 publications

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“…A similar problem was found in [26] in the investigation of 2 dimensional instantons in noncommutative CP (n) model. Indeed, when looking for a solution leading to a singular instanton in the θ → 0 limit, these authors find that selfduality was satisfied up to a vacuum projector exactly as what happens with the r.h.s.…”

Section: 'T Hooft Ansatz In Noncommutative Spacesupporting

confidence: 72%

Comments on the U(2) noncommutative instanton

Correa¹,

Lozano²,

Moreno³

et al. 2001

Physics Letters B

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We discuss the 't Hoof ansatz for instanton solutions in noncommutative U (2) Yang-Mills theory. We show that the extension of the ansatz leading to singular solutions in the commutative case, yields to non self-dual (or self-antidual) configurations in noncommutative space-time. A proposal leading to selfdual solutions with Q = 1 topological charge (the equivalent of the regular BPST ansatz) can be engineered, but in that case the gauge field and the curvature are not Hermitian (although the resulting Lagrangian is real).

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Section: 'T Hooft Ansatz In Noncommutative Spacesupporting

confidence: 72%

Comments on the U(2) noncommutative instanton

Correa¹,

Lozano²,

Moreno³

et al. 2001

Physics Letters B

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“…If we choose polynomials of at maximal degree q, the energy of the configuration will be E = 8πq, independently of the gauge group. To illustrate this fact we sketch the following U (2) example: 13) which is of infinite rank in H. Still, the energy (5.6) is readily computed with the result of 8πq.…”

Section: Static Solutionsmentioning

confidence: 99%

Noncommutative multi-solitons in 2+1 dimensions

Lechtenfeld

Popov

2001

J. High Energy Phys.

101

160

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The study of noncommutative solitons is greatly facilitated if the field equations are integrable, i.e. result from a linear system. For the example of a modified but integrable U (n) sigma model in 2+1 dimensions we employ the dressing method to construct explicit multi-soliton configurations on noncommutative R 2,1 . These solutions, abelian and nonabelian, feature exact time-dependence for any value of the noncommutativity parameter θ and describe various lumps of finite energy in relative motion. We discuss their scattering properties and prove asymptotic factorization for large times.

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“…Focusing on the BPS states though, saturation of the bound on the energy is obtained when F + (P ) = 0. As first shown in [22], solutions are not difficult to find; any Hermitian projector constructed from an (n + 1)−vector W whose components are holomorphic polynomials in z will satisfy the above BPS equation. These are precisely the noncommutative extension of the instanton solutions of the conventional CP N sigma model.…”

Section: With Eq(41) As a Starting Point A Reparameterization Of Tmentioning

confidence: 95%

Transmogrifying fuzzy vortices

Murugan¹,

Millner²

2004

J. High Energy Phys.

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We show that the construction of vortex solitons of the noncommutative Abelian-Higgs model can be extended to a critically coupled gauged linear sigma model with Fayet-Illiopolous D-terms. Like its commutative counterpart, this fuzzy linear sigma model has a rich spectrum of BPS solutions. We offer an explicit construction of the degree−k static semilocal vortex and study in some detail the infinite coupling limit in which it descends to a degree−k CP N instanton. This relation between the fuzzy vortex and noncommutative lump is used to suggest an interpretation of the noncommutative sigma model soliton as tilted D-strings stretched between an NS5-brane and a stack of D3-branes in type IIB superstring theory.

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The CP(n) model on noncommutative plane

Cited by 44 publications

References 53 publications

Comments on the U(2) noncommutative instanton

Comments on the U(2) noncommutative instanton

Noncommutative multi-solitons in 2+1 dimensions

Transmogrifying fuzzy vortices

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