G. M. Sotkov

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.

T-duality of axial and vector dyonic integrable models

Abstract A general construction of affine nonabelian (NA)-Toda models in terms of the axial and vector gauged two loop WZNW model is discussed. They represent integrable perturbations of the conformal σ-models (with tachyons included) describing (charged) black hole type string backgrounds. We study the off-critical T-duality between certain families of axial and vector type 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 T-selfdual torsionless NA-Toda models and their zero curvature representation.

Electrically charged topological solitons

Abstract 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.

T-duality in 2D integrable models

The non-conformal analogue of Abelian T-duality transformations relating pairs of axial and vector integrable models from the non-Abelian affine Toda family is constructed and studied in detail.

Vertex operators and soliton solutions of affine Toda model with U(2) symmetry

The symmetry structure of the non-Abelian affine Toda model based on the coset SL(3)/SL(2) ⊗ U(1) is studied. It is shown that the model possess non-Abelian Noether symmetry closing into a q-deformed SL(2) ⊗ U(1) algebra. Specific two-vertex soliton solutions are constructed.

Multicharged dyonic integrable models

Abstract We introduce and study new integrable models (IMs) of An(1)-nonabelian Toda type which admit U(1)⊗U(1) charged topological solitons. They correspond to the symmetry breaking SU(n+1)→SU(2)⊗SU(2)⊗U(1)n−2 and are conjectured to describe charged dyonic domain walls of N=1 SU(n+1) SUSY gauge theory in large n limit. It is shown that this family of relativistic IMs corresponds to the first negative grade q=−1 member of a dyonic hierarchy of generalized cKP type. The explicit relation between the 1-soliton solutions (and the conserved charges as well) of the IMs of grades q=−1 and q=2 is found. The properties of the IMs corresponding to more general symmetry breaking SU(n+1)→SU(2)⊗p⊗U(1)n−p as well as IM with global SU(2) symmetries are discussed.

Soliton spectrum of integrable models with local symmetries

The soliton spectrum (massive and massless) of a family of integrable models with local U(1) and U(1) ? U(1) symmetries is studied. These models represent relevant integrable deformations of SL(2, ) ? U(1)n?1-WZW and SL(2, ) ? SL(2, ) ? U(1)n?2-WZW models. Their massless solitons appear as specific topological solutions of the U(1)- (or U(1) ? U(1)-) CFTs. The nonconformal analog of the GKO-coset formula is derived and used in the construction of the composite massive solitons of the ungauged integrable models.

Axial Vector Duality in Affine NA Toda Models

A general and systematic construction of Non Abelian affine Toda models and its symmetries is proposed in terms of its underlying Lie algebraic structure. It is also shown that such class of two dimensional integrable models naturally leads to the construction of a pair of actions related by T-duality transformations

Solitons with Isospin

We study the symmetries of the soliton spectrum of a pair of T-dual integrable models, invariant under global SL(2)q⊗U(1) transformations. They represent an integrable perturbation of the reduced Gepner parafermions, based on certain gauged SL(3)–WZW model. Their (semiclassical) topological soliton solutions, carrying isospin and belonging to the root of unity representations of q-deformed SU(2)q-algebra are obtained. We derive the semiclassical particle spectrum of these models, which is further used to prove their T-duality properties.

T-duality in Affine NA Toda Models

The construction of non-Abelian affine Toda models is discussed in terms of its underlying Lie algebraic structure. It is shown that a subclass of such non-conformal two-dimensional integrable models naturally leads to the construction of a pair of actions, which share the same spectra and are related by canonical transformations.