T-duality of axial and vector dyonic integrable models

A general construction of affine Non Abelian (NA) - Toda models in terms of axial and vector gauged two loop WZNW model is discussed. They represent {\it integrable perturbations} of the conformal $\sigma$-models (with tachyons included) describing (charged) black hole type string backgrounds. We study the {\it off-critical} T-duality between certain families of axial and vector type of integrable models for the case of affine NA- Toda theories with one global U(1) symmetry. In particular we find the Lie algebraic condition defining a subclass of {\it T-selfdual} torsionless NA Toda models and their zero curvature representation.Comment: 20 pages, latex, no figures,improvments in the text of Sects.1,2 and 6;typos corrected,references added, to appear in Ann. of Physics (NY

Dyonic Integrable Models

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.Comment: Latex 30 pages, corrected some typo

Abelian Toda field theories on the noncommutative plane

Generalizations of GL(n) abelian Toda and $\widetilde{GL}(n)$ abelian affine Toda field theories to the noncommutative plane are constructed. Our proposal relies on the noncommutative extension of a zero-curvature condition satisfied by algebra-valued gauge potentials dependent on the fields. This condition can be expressed as noncommutative Leznov-Saveliev equations which make possible to define the noncommutative generalizations as systems of second order differential equations, with an infinite chain of conserved currents. The actions corresponding to these field theories are also provided. The special cases of GL(2) Liouville and $\widetilde{GL}(2)$ sinh/sine-Gordon are explicitly studied. It is also shown that from the noncommutative (anti-)self-dual Yang-Mills equations in four dimensions it is possible to obtain by dimensional reduction the equations of motion of the two-dimensional models constructed. This fact supports the validity of the noncommutative version of the Ward conjecture. The relation of our proposal to previous versions of some specific Toda field theories reported in the literature is presented as well.Comment: v3 30 pages, changes in the text, new sections included and references adde

Electrically Charged Topological Solitons

Two new families of T-Dual integrable models of dyonic type are constructed. They represent specific $A_n^{(1)}$ singular Non-Abelian Affine Toda models having U(1) global symmetry. Their 1-soliton spectrum contains both neutral and U(1) charged topological solitons sharing the main properties of 4-dimensional Yang-Mills-Higgs monopoles and dyons. The semiclassical quantization of these solutions as well as the exact counterterms and the coupling constant renormalization are studied.Comment: 40 pages, latex, typos corrected in eq. (2.3), new section on spin of solitons added, extended discussion on T-duality relation between axial and vector topological theta terms in new subsection 2.