Wess–Zumino–Witten and fermion models in noncommutative space

Moreno, E.C.; Schaposnik, F

doi:10.1016/s0550-3213(00)00702-1

Cited by 33 publications

(44 citation statements)

References 23 publications

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“…In the noncommutative case the bosonization of a single massless Dirac fermion produces a noncommutative U(1) WZW model [35], which becomes free only in the commutative limit. Moreover, the U(1) subgroup of U(N ) does no longer decouple [36], so that N noncommuting free massless fermions are related to a noncommutative WZW model for a scalar in U(N ).…”

Section: Noncommutative Integrable Sigma Model In 2+1 Dimensionsmentioning

confidence: 99%

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: Noncommutative Integrable Sigma Model In 2+1 Dimensionsmentioning

confidence: 99%

Integrable noncommutative sine-Gordon model

et al. 2005

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“…The bosonization process of the NC extension of the usual Thirring interaction performed in [27,28] considers only the interaction term j (1) µ j (1) µ interaction corresponds to a bosonized theory whose dynamics is governed by a NC WZW action plus a bosonized Thirring coupling and a NC cosine potential [28], then the bosonized model resembles one of the sectors, say g sector, of the Grisaru-Penati model (3.18). It is expected that the bosonization procedure of the NCMT 1 model will provide a bosonic action of the Lechtenfeld et al type model (3.11).…”

Section: Jhep03(2005)037mentioning

confidence: 99%

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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“…It is an interesting question to investigate whether this holds to all orders. In this context, we recall that the 2-dimensional commutative and noncommutative WZW models are known to be equivalent not just in their gauge structure but also in their action [43,44].…”

Section: Sw Map In the U (1) Casementioning

confidence: 99%

Seiberg-Witten maps from the point of view of consistent deformations of gauge theories

Barnich

Henneaux

Grigoriev

2001

J. High Energy Phys.

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Noncommutative versions of theories with a gauge freedom define (when they exist) consistent deformations of their commutative counterparts. General aspects of Seiberg-Witten maps are discussed from this point of view. In particular, the existence of the Seiberg-Witten maps for various noncommutative theories is related to known cohomological theorems on the rigidity of the gauge symmetries of the commutative versions. In technical terms, the Seiberg-Witten maps define canonical transformations in the antibracket that make the solutions of the master equation for the commutative and noncommutative versions coincide in their antifield-dependent terms. As an illustration, the on-shell reducible noncommutative Freedman-Townsend theory is considered.

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Wess–Zumino–Witten and fermion models in noncommutative space

Cited by 33 publications

References 23 publications

Integrable noncommutative sine-Gordon model

Integrable noncommutative sine-Gordon model

Non-commutative solitons and strong-weak duality

Seiberg-Witten maps from the point of view of consistent deformations of gauge theories

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