From noncommutative bosonization to S-duality

Núñez, Carlos; Olsen, Kasper; Schiappa, Ricardo

doi:10.1088/1126-6708/2000/07/030

Cited by 33 publications

(55 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…∂φ∂φ + γ(1 − cos φ)] and replace ordinary products by * -products [12]. However, since the currents obtained as a natural extension of the ordinary ones are not conserved, the corresponding system is not guaranteed to be integrable.…”

Section: Discussionmentioning

confidence: 99%

An integrable noncommutative version of the sine-Gordon system

Grisaru

Penati

2003

Nuclear Physics B

View full text Add to dashboard Cite

Using the bicomplex approach we discuss a noncommutative system in two-dimensional Euclidean space. It is described by an equation of motion which reduces to the ordinary sine-Gordon equation when the noncommutation parameter is removed, plus a constraint equation which is nontrivial only in the noncommutative case. We show that the system has an infinite number of conserved currents and we give the general recursive relation for constructing them. For the particular cases of lower spin nontrivial currents we work out the explicit expressions and perform a direct check of their conservation. These currents reduce to the usual sine-Gordon currents in the commutative limit. We find classical "localized" solutions to first order in the noncommutativity parameter and describe the Backlund transformations for our system. Finally, we comment on the relation of our noncommutative system to the commutative sine-Gordon system.

show abstract

Section: Discussionmentioning

confidence: 99%

An integrable noncommutative version of the sine-Gordon system

Grisaru

Penati

2003

Nuclear Physics B

View full text Add to dashboard Cite

show abstract

“…In particular, in the bosonization process of NCMT 1,2 models and their multi-fermion extensions, initiated in [28] by directly starring the usual Thirring interaction, we believe that a careful understanding of the star-localized NC Noether symmetries, as well as the classical soliton spectrum would be desirable.…”

Section: Jhep03(2005)037mentioning

confidence: 99%

Non-commutative solitons and strong-weak duality

Blas

Carrion

Rojas

2005

J. High Energy Phys.

View full text Add to dashboard Cite

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

show abstract

“…(15) when the Dirac operator is taken in the adjoint representation, as defined in eq. (13). The interaction term S I of the action S[ψ, ψ, A] (eq.…”

Section: Perturbative Effective Actionmentioning

confidence: 99%

Wess–Zumino–Witten and fermion models in noncommutative space

Moreno

Schaposnik

2001

Nuclear Physics B

View full text Add to dashboard Cite

We analyze the connection between Wess-Zumino-Witten and free fermion models in two-dimensional noncommutative space. Starting from the computation of the determinant of the Dirac operator in a gauge field background, we derive the corresponding bosonization recipe studying, as an example, bosonization of the U (N ) Thirring model. Concerning the properties of the noncommutative Wess-Zumino-Witten model, we construct an orbit-preserving transformation that maps the standard commutative WZW action into the noncommutative one.

show abstract

From noncommutative bosonization to S-duality

Cited by 33 publications

References 27 publications

An integrable noncommutative version of the sine-Gordon system

An integrable noncommutative version of the sine-Gordon system

Non-commutative solitons and strong-weak duality

Wess–Zumino–Witten and fermion models in noncommutative space

Contact Info

Product

Resources

About