Connection between the affine and conformal affine Toda models and their Hirota solution

Constantinidis, C. P.; Ferreira, L. A.; Gomes, J. F.; Zímerman, A. H.

doi:10.1016/0370-2693(93)91712-v

Cited by 25 publications

(73 citation statements)

References 20 publications

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“…Then, the resulting model is not conformally invariant and we refer to it as the Generalized non-abelian Affine Toda (G-AT). All this is a generalization of what occurs in the abelian Conformal Affine Toda models [14].…”

Section: Introductionmentioning

confidence: 63%

“…The improved stress tensor (3.13) satisfies 14) which is a centreless Virasoro algebra too; notice that the Virasoro algebra generated by L(x) might have a central extension proportional to Tr(Q 2 s ), but, for the particular choice (C.1), it vanishes. With respect to L(x), the components of the current J R (x) whose grade is j ∈ Z Z transform as primary fields of conformal weight 1 − j/l, with the exception of the component Tr (CJ R (x)) whose transformation is…”

Section: Conformal Invariance Of the G-cat Modelsmentioning

confidence: 99%

“…Therefore the solutions for η are of the form 21) and, for every regular solution, the term e lη can be eliminated by a coordinate transformation, like in the usual CAT models [14]. In fact, for regular solutions, we can define the coordinate transformation…”

Section: Conformal Invariance Of the G-cat Modelsmentioning

confidence: 99%

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Solitons, τ-functions and hamiltonian reduction for non-Abelian conformal affine Toda theories

1995

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We consider the Hamiltonian reduction of the two-loop Wess-Zumino-Novikov-Witten model (WZNW) based on an untwisted affine Kac-Moody algebraĜ. The resulting reduced models, called Generalized Non-Abelian Conformal Affine Toda (G-CAT), are conformally invariant and a wide class of them possesses soliton solutions; these models constitute non-abelian generalizations of the Conformal Affine Toda models. Their general solution is constructed by the Leznov-Saveliev method. Moreover, the dressing transformations leading to the solutions in the orbit of the vacuum are considered in detail, as well as the τ -functions, which are defined for any integrable highest weight representation ofĜ, irrespectively of its particular realization. When the conformal symmetry is spontaneously broken, the G-CAT model becomes a generalized Affine Toda model, whose soliton solutions are constructed. Their masses are obtained exploring the spontaneous breakdown of the conformal symmetry, and their relation to the fundamental particle masses is discussed.

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Section: Introductionmentioning

confidence: 63%

Section: Conformal Invariance Of the G-cat Modelsmentioning

confidence: 99%

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Solitons, τ-functions and hamiltonian reduction for non-Abelian conformal affine Toda theories

1995

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“…The soliton solutions for the SU(N ) Affine Toda field theories were first constructed by Hollowood [31] using the Hirota method. The generalization of the construction to AT models associated to other algebras were presented in [32][33][34][35][36] using the Hirota method, and in [26,[37][38][39] using the Leznov-Saveliev method and the representation theory of Kac-Moody algebras based on vertex operators. The Hirota method is perhaps the most efficient procedure for constructing explicit analytical soliton solutions.…”

Section: The Exact Soliton Solutions Of the Integrable Affine Toda Momentioning

confidence: 99%

Quasi-integrable deformations of the SU(3) Affine Toda theory

Ferreira

Klimas

Zakrzewski

2016

J. High Energ. Phys.

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Abstract:We consider deformations of the SU(3) Affine Toda theory (AT) and investigate the integrability properties of the deformed theories. We find that for some special deformations all conserved quantities change to being conserved only asymptotically, i.e. in the process of the scattering of two solitons these charges do vary in time, but they return, after the scattering, to the values they had prior to the scattering. This phenomenon, which we have called quasi-integrability, is related to special properties of the two-soliton solutions under space-time parity transformations. Some properties of the AT solitons are discussed, especially those involving interesting static multi-soliton solutions. We support our analytical studies with detailed numerical ones in which the time evolution has been simulated by the 4th order Runge-Kutta method. We find that for some perturbations the solitons repel and for the others they form a quasi-bound state. When we send solitons towards each other they can repel when they come close together with or without 'flipping' the fields of the model. The solitons radiate very little and appear to be stable. These results support the ideas of quasi-integrability, i.e. that many effects of integrability also approximately hold for the deformed models.

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“…Such solutions were constructed first for the A (1) n theories, and although they are not real they nevertheless have real energy. Further soliton solutions were found for other Lie algebras in [18][19][20][21][22][23][24], with the most general solution being given in [18,19], and the energy and momentum were found to be real in these cases also. The masses of the single soliton solutions were seen to form the left Perron-Frobenius eigenvector of the Cartan matrix of g [18], while the masses of the fundamental excitations formed the right Perron-Frobenius eigenvector.…”

Section: Introductionmentioning

confidence: 99%