Dyonic integrable models

Abstract

A class of non abelian affine Toda models arising from the axial gauged two-loop WZW model is presented. Their zero curvature representation is constructed in terms of a graded Kac-Moody algebra. It is shown that the discrete multivacua structure of the potential together with non abelian nature of the zero grade subalgebra allows soliton solutions with non trivial electric and topological charges. The dressing transformation is employed to explicitly construct one and two soliton solutions and their bound states in terms of the tau functions. A discussion of the classical spectra of such solutions and the time delays are given in detail.

Solitons with isospin

“…The second relation is based on the following identities: It should be noted that topological charges can be defined for certain "non-isometric" fields too( see [16] for relevant examples), that have properties of "angular" variables. Since T-duality keeps unchanged these fields, the corresponding "non-isometric" topological charges of axial and vector models do coincide.…”

“…The second difference concerns their symmetries: the abelian ATFT's do not have Noether symmetries, while the non-abelian ones present manifest global symmetries, say U (1) ⊗k or SU(2) ⊗ U(1) ⊗s , etc. [16], [17], [18]. Another important feature of the non-abelian ATFT's is that they always appear in T-dual pairs of IM's, related by specific canonical transformations [19].…”

“…While the quantization of the abelian ATFT's is well developed, it is not the case of the non-abelian ATFT's. Their rich symmetry structure together with the complicated counterterms needed in their quantum analysis [20], make the problem of their quantization difficult and rather different from the abelian ATFT's [16], [21]. From the other side, due to their integrability, a set of stable nonperturbative classical solutions (solitons and breathers) of these IM's have been recently constructed [15], [16], [17], [22].…”

“…Their rich symmetry structure together with the complicated counterterms needed in their quantum analysis [20], make the problem of their quantization difficult and rather different from the abelian ATFT's [16], [21]. From the other side, due to their integrability, a set of stable nonperturbative classical solutions (solitons and breathers) of these IM's have been recently constructed [15], [16], [17], [22]. This suggests that one can follow further the semiclassical methods [24] of quantization of these solutions in order to derive their nonperturbative particle spectrum, S-matrices, form-factors, etc.…”

“…As we have shown in our recent paper [17], these integrable theories represent the simplest example of models invariant under global transformations from the non-abelian q-deformed algebra SL(2) q ⊗ U(1) with q = exp(iβ 2 0 ). Note that the other known NA-ATFT's as Homogeneous Sine-Gordon models [15], A (1) n -dyonic IM's [16] and the Fateev's IM's [21] admit instead only abelian U (1) ⊗s , s = 1, 2, · · · global (or local) symmetries. As a consequence of their unusual symmetry structure, both IM's (1.1) and (1.2) possess semiclassical Bohr-Sommerfeld (BS) topological solitons carrying isospin I, the U(1) charge Q and belonging to certain roots of unity representations q 2(k+3) = 1 of SU(2) q -algebra as shown in Sect.…”