Noncommutative integrable field theories in 2d

Cabrera-Carnero, I.; Moriconi, Marco

doi:10.1016/j.nuclphysb.2003.09.014

Cited by 44 publications

(64 citation statements)

References 19 publications

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“…Usually, time-space noncommutativity adversely affects the causality and unitarity of the S-matrix (see, e.g. [21,22,17]), even in the presence of an infinite number of local conservation laws. In contrast, the model described here seems to possess an Smatrix which is causal and factorized, as we checked for all tree-level 2 → 2 processes both in the Yang and Leznov formulations.…”

Section: Discussionmentioning

confidence: 99%

“…In 1+1 dimensions, noncommutative models have not yet been considered extensively, primarily because in this situation time is necessarily a noncommutative coordinate, which appears to compromise the causality and unitarity of the theory [18,19,20,21,17]. However, one may hope that a huge underlying symmetry improves the situation in systems which allow for a Lax-pair formulation and so feature an infinite chain of conserved charges.…”

Section: Introductionmentioning

confidence: 99%

“…Previous suggestions for noncommutative sine-Gordon models can be found in [22,21]. In particular, in [22] a model was proposed which describes the dynamics of a complex scalar field by a couple of equations of motion.…”

Section: Introductionmentioning

confidence: 99%

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Integrable noncommutative sine-Gordon model

et al. 2005

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Requiring an infinite number of conserved local charges or the existence of an underlying linear system does not uniquely determine the Moyal deformation of 1+1 dimensional integrable field theories. As an example, the sine-Gordon model may be obtained by dimensional and algebraic reduction from 2+2 dimensional self-dual U(2) Yang-Mills through a 2+1 dimensional integrable U(2) sigma model, with some freedom in the noncommutative extension of this algebraic reduction. Relaxing the latter from U(2) → U(1) to U(2) → U(1)×U(1), we arrive at novel noncommutative sine-Gordon equations for a pair of scalar fields. The dressing method is employed to construct its multi-soliton solutions. Finally, we evaluate various tree-level amplitudes to demonstrate that our model possesses a factorizable and causal S-matrix in spite of its time-space noncommutativity.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Integrable noncommutative sine-Gordon model

et al. 2005

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“…The zero-curvature condition encodes integrability even in the NC extension of integrable models [5], then we may conclude that the (Bosonic) NCMT 1,2 theories are integrable and infinite conserved charges may be constructed for them.…”

Section: Jhep03(2005)037mentioning

confidence: 95%

Non-commutative solitons and strong-weak duality

Blas

Carrion

Rojas

2005

J. High Energy Phys.

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Some properties of the non-commutative versions of the sine-Gordon model (NCSG) and the corresponding massive Thirring theories (NCMT) are studied. Our method relies on the NC extension of integrable models and the master Lagrangian approach to deal with dual theories. The master Lagrangians turn out to be the NC versions of the so-called affine Toda model coupled to matter fields (NCATM) associated to the group GL(2), in which the Toda field belongs to certain representations of either U (1)xU (1) or U (1) C corresponding to the Lechtenfeld et al. (NCSG 1 ) or Grisaru-Penati (NCSG 2 ) proposals for the NC versions of the sine-Gordon model, respectively. Besides, the relevant NCMT 1,2 models are written for two (four) types of Dirac fields corresponding to the Moyal product extension of one (two) copy(ies) of the ordinary massive Thirring model. The NCATM 1,2 models share the same one-soliton (real Toda field sector of model 2) exact solutions, which are found without expansion in the NC parameter θ for the corresponding Toda and matter fields describing the strong-weak phases, respectively. The correspondence NCSG 1 ↔ NCMT 1 is promising since it is expected to hold on the quantum level. * ⋆ e −iϕ + ⋆ − 2 .(3.11)In this way we have re-derived the Lechtenfeld et al. action (NCSG 1

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“…The methods outlined in this talk have also been applied successfully towards the construction and study of various other noncommutative field configurations (see for example [10,11,12,13] and references therein 2 ). In my group, in particular, we have investigated [14,15,16,17,18] • …”

Section: D=4+0: Instantons In Noncommutative Yang-millsmentioning

confidence: 99%

Noncommutative instantons and solitons

Lechtenfeld

2004

Fortschritte der Physik

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I explain how to construct noncommutative BPS configurations in four and lower dimensions by solving linear matrix equations. Examples are instantons in D=4 Yang-Mills, monopoles in D=3 Yang-Mills-Higgs, and (moving) solitons in D=2+1 YangMills-Higgs. Some emphasis is on the latter as a showcase for the dressing method. Self-duality and BPS equationsIn this talk I shall present a powerful method for and results of constructing classical field configurations with finite action or energy in four-dimensional noncommutative gauge theory and its lower-dimensional descendants:I am setting up the formalism in such a way that it is completely transparent to the (Moyal-type) noncommutative deformation. In other words, the noncommutative equations below differ from the commutative ones merely in the interpretation of the symbols or their product (stars are suppressed). This will be briefly explained in Section 6. The Yang-Mills field equations are implied by first-order (self-duality or BPS) equations:where F and φ are u(n) valued and Greek indices run from 1 to 4 while Latin ones stop at 3. In complex coordinates (note the signs!) y = x 1 +ix 2 and z = x 3 ∓ix 4 the self-duality equationwhere the upper and lower signs belong to the signatures (4,0) and (2,2), respectively. Dimensional reduction to D=3 is accomplished via

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Noncommutative integrable field theories in 2d

Cited by 44 publications

References 19 publications

Integrable noncommutative sine-Gordon model

Integrable noncommutative sine-Gordon model

Non-commutative solitons and strong-weak duality

Noncommutative instantons and solitons

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