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.

T-duality of axial and vector dyonic integrable models

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 sigma -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. (C) 2001 Academic Press.

A class of mixed integrable models

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Higher order Painleve equations and their symmetries via reductions of a class of integrable models

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Super-WZNW with reductions to supersymmetric and fermionic integrable models

A systematic construction for an action describing a class of supersymmetric integrable models as well as for pure fermionic theories is discussed in terms of the gauged WZNW model associated to half integer graded affine Kac-Moody algebras. Explicit examples of the N = 1. 2 super-sinh(sine)-Gordon models are discussed in detail. Pure fermionic theories arises for cosets sl(p, 1)/sl(p) circle times u(1) when a maximal kernel condition is fulfilled. The integrability condition for such models is discussed and it is shown that the simplest example when p = 2 (cads to the constrained Bukhvostov-Lipatov, Thirring, scalar massive and pseudo-scalar massless Gross-Neveu models. (C) 2009 Published by Elsevier B.V.

Gravitational interactions of integrable models

We couple non-linear sigma-models to Liouville gravity, showing that integrability properties of symmetric space models still hold for the matter sector. Using similar arguments for the fermionic counterpart, namely Gross-Neveu-type models, we verify that such conclusions must also hold for them, as recently suggested.

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,ℝ) ⊗U(1) n-1-WZW and SL(2,ℝ) ⊗ SL(2,ℝ) ⊗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. © SISSA/ISAS 2002.

Multicharged dyonic integrable models

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. © 2002 Elsevier Science B.V. All rights reserved.

Multiseries Lie groups and asymptotic modules for characterizing and solving integrable models

A multiseries integrable model (MSIM) is defined as a family of compatible flows on an infinite-dimensional Lie group of N-tuples of formal series around N given poles on the Riemann sphere. Broad classes of solutions to a MSIM are characterized through modules over rings of rational functions, called asymptotic modules. Possible ways for constructing asymptotic modules are Riemann-Hilbert and ∂̄ problems. When MSIM's are written in terms of the group coordinates, some of them can be contracted into standard integrable models involving a small number of scalar functions only. Simple contractible MSIM's corresponding to one pole, yield the Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy. Two-pole contractible MSIM's are exhibited, which lead to a hierarchy of solvable systems of nonlinear differential equations consisting of (2 + 1) -dimensional evolution equations and of quite strong differential constraints. © 1989 American Institute of Physics.

Integrable Models: from Dynamical Solutions to String Theory

We review the status of integrable models from the point of view of their dynamics and integrability conditions. A few integrable models are discussed in detail. We comment on the use it is made of them in string theory. We also discuss the SO(6) symmetric Hamiltonian with SO(6) boundary. This work is especially prepared for the 70th anniversaries of Andr, Swieca (in memoriam) and Roland Koberle.

Monoidal categories for the physics of integrable models

Scopo di questa tesi é di evidenziare le connessioni tra le categorie monoidali, l'equazione di Yang-Baxter e l’integrabilità di alcuni modelli. Oggetto prinacipale del nostro lavoro é stato il monoide di Frobenius e come sia connesso alle C∗-algebre. In questo contesto la totalità delle dimostrazioni sfruttano la strumentazione dell'algebra diagrammatica. Nel corso del lavoro di tesi sono state riprodotte tali dimostrazioni tramite il più familiare linguaggio dell’algebra multilineare allo scopo di rendere più fruibili questi risultati ad un raggio più ampio di potenziali lettori.

Classical integrable N=1 and N=2 super sinh-Gordon models with jump defects

The structure of integrable field theories in the presence of jump defects is discussed in terms of boundary functions under the Lagrangian formalism. Explicit examples of bosonic and fermionic theories are considered. In particular, the boundary functions for the N = 1 and N = 2 super sinh-Gordon models are constructed and shown to generate the Backlund transformations for its soliton solutions. As a new and interesting example, a solution with an incoming boson and an outgoing fermion for the N = 1 case is presented. The resulting integrable models are shown to be invariant under supersymmetric transformation.

On the construction of correlation functions for the integrable supersymmetric fermion models

We review the recent progress on the construction of the determinant representations of the correlation functions for the integrable supersymmetric fermion models. The factorizing F-matrices (or the so-called F-basis) play an important role in the construction. In the F-basis, the creation (and the annihilation) operators and the Bethe states of the integrable models are given in completely symmetric forms. This leads to the determinant representations of the scalar products of the Bethe states for the models. Based on the scalar products, the determinant representations of the correlation functions may be obtained. As an example, in this review, we give the determinant representations of the two-point correlation function for the U-q(gl(2 vertical bar 1)) (i.e. q-deformed) supersymmetric t-J model. The determinant representations are useful for analyzing physical properties of the integrable models in the thermodynamical limit.