The sine-Gordon model with integrable defects revisited

Application of our algebraic approach to Liouville integrable defects is proposed for the sine-Gordon model. Integrability of the model is ensured by the underlying classical r-matrix algebra. The first local integrals of motion are identified together with the corresponding Lax pairs. Continuity conditions imposed on the time components of the entailed Lax pairs give rise to the sewing conditions on the defect point consistent with Liouville integrability.Comment: 24 pages Latex. Minor modifications, added comment

Free Field Realization of Vertex Operators for Level Two Modules of Uq(sl(2)^)U_q(\hat{sl(2)})

Free field relization of vertex operators for lvel two modules of $U_q(\hat{sl(2)})$ is shown through the free field relization of the modules given by Idzumi in Ref.[4,5]. We constructed types I and II vertex operators when the spin of the addociated evaluation modules is 1/2 and typ II's for the spin 1.Comment: 15 pages, to appear in J.Phys.A:Math and Genera

Interplay between Zamolodchikov-Faddeev and Reflection-Transmission algebras

We show that a suitable coset algebra, constructed in terms of an extension of the Zamolodchikov-Faddeev algebra, is homomorphic to the Reflection-Transmission algebra, as it appears in the study of integrable systems with impurity.Comment: 8 pages; a misprint in eq. (2.14) and (2.15) has been correcte

Form factors of boundary fields for A(2)-affine Toda field theory

In this paper we carry out the boundary form factor program for the A(2)-affine Toda field theory at the self-dual point. The latter is an integrable model consisting of a pair of particles which are conjugated to each other and possessing two bound states resulting from the scattering processes 1 +1 -> 2 and 2+2-> 1. We obtain solutions up to four particle form factors for two families of fields which can be identified with spinless and spin-1 fields of the bulk theory. Previously known as well as new bulk form factor solutions are obtained as a particular limit of ours. Minimal solutions of the boundary form factor equations for all A(n)-affine Toda field theories are given, which will serve as starting point for a generalisation of our results to higher rank algebras.Comment: 24 pages LaTeX, 1 figur

Dyons in N=4 Supersymmetric Theories and Three-Pronged Strings

We construct and explore BPS states that preserve 1/4 of supersymmetry in N=4 Yang-Mills theories. Such states are also realized as three-pronged strings ending on D3-branes. We correct the electric part of the BPS equation and relate its solutions to the unbroken abelian gauge group generators. Generic 1/4-BPS solitons are not spherically symmetric, but consist of two or more dyonic components held apart by a delicate balance between static electromagnetic force and scalar Higgs force. The instability previously found in three-pronged string configurations is due to excessive repulsion by one of these static forces. We also present an alternate construction of these 1/4-BPS states from quantum excitations around a magnetic monopole, and build up the supermultiplet for arbitrary (quantized) electric charge. The degeneracy and the highest spin of the supermultiplet increase linearly with a relative electric charge. We conclude with comments.Comment: 33 pages, two figures, LaTex, a footnote added, the figure caption of Fig.2 expanded, one more referenc

Supersymmetric WZW σ\sigma Model on Full and Half Plane

We study classical integrability of the supersymmetric U(N) $\sigma$ model with the Wess-Zumino-Witten term on full and half plane. We demonstrate the existence of nonlocal conserved currents of the model and derive general recursion relations for the infinite number of the corresponding charges in a superfield framework. The explicit form of the first few supersymmetric charges are constructed. We show that the considered model is integrable on full plane as a concequence of the conservation of the supersymmetric charges. Also, we study the model on half plane with free boundary, and examine the conservation of the supersymmetric charges on half plane and find that they are conserved as a result of the equations of motion and the free boundary condition. As a result, the model on half plane with free boundary is integrable. Finally, we conclude the paper and some features and comments are presented.Comment: 12 pages. submitted to IJMP

Liouville integrable defects: the non-linear Schrodinger paradigm

A systematic approach to Liouville integrable defects is proposed, based on an underlying Poisson algebraic structure. The non-linear Schrodinger model in the presence of a single particle-like defect is investigated through this algebraic approach. Local integrals of motions are constructed as well as the time components of the corresponding Lax pairs. Continuity conditions imposed upon the time components of the Lax pair to all orders give rise to sewing conditions, which turn out to be compatible with the hierarchy of charges in involution. Coincidence of our results with the continuum limit of the discrete expressions obtained in earlier works further confirms our approach.Comment: 22 pages, Latex. Minor misprints correcte

Boundary form factors of the sinh-Gordon model with Dirichlet boundary conditions at the self-dual point

In this manuscript we present a detailed investigation of the form factors of boundary fields of the sinh-Gordon model with a particular type of Dirichlet boundary condition, corresponding to zero value of the sinh-Gordon field at the boundary, at the self-dual point. We follow for this the boundary form factor program recently proposed by Z. Bajnok, L. Palla and G. Takaks in hep-th/0603171, extending the analysis of the boundary sinh-Gordon model initiated there. The main result of the paper is a conjecture for the structure of all n-particle form factors of two particular boundary operators in terms of elementary symmetric polynomials in certain functions of the rapidity variables. In addition, form factors of boundary "descendant" fields have been constructedComment: 14 pages LaTex. Version to appear in J. Phys.

A multisymplectic approach to defects in integrable classical field theory

We introduce the concept of multisymplectic formalism, familiar in covariant field theory, for the study of integrable defects in 1+1 classical field theory. The main idea is the coexistence of two Poisson brackets, one for each spacetime coordinate. The Poisson bracket corresponding to the time coordinate is the usual one describing the time evolution of the system. Taking the nonlinear Schr\"odinger (NLS) equation as an example, we introduce the new bracket associated to the space coordinate. We show that, in the absence of any defect, the two brackets yield completely equivalent Hamiltonian descriptions of the model. However, in the presence of a defect described by a frozen B\"acklund transformation, the advantage of using the new bracket becomes evident. It allows us to reinterpret the defect conditions as canonical transformations. As a consequence, we are also able to implement the method of the classical r matrix and to prove Liouville integrability of the system with such a defect. The use of the new Poisson bracket completely bypasses all the known problems associated with the presence of a defect in the discussion of Liouville integrability. A by-product of the approach is the reinterpretation of the defect Lagrangian used in the Lagrangian description of integrable defects as the generating function of the canonical transformation representing the defect conditions