Semiclassical analysis of defect sine-Gordon theory

The classical sine-Gordon model is a two-dimensional integrable field theory, with particle like solutions the so-called solitons. Using its integrability one can define its quantum version without the process of canonical quantization. This bootstrap method uses the fundamental propterties of the model and its quantum features in order to restrict the structure of the scattering matrix as far as possible. The classical model can be extended with integrable discontinuities, purely transmitting jump-defects. Then the quantum version of the extended model can be determined via the bootstrap method again. But the outcoming quantum theory contains the so-called CDD uncertainity. The aim of this article is to carry throw the semiclassical approximation in both the classical and the quantum side of the defect sine-Gordon theory. The CDD ambiguity can be restricted by comparing the two results. The relation between the classical and quantum parameters as well as the resoncances appeared in the spectrum are other objectives

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

Classical Integrable N=1 and N=2N= 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.Comment: talk presented at the V International Symposium on Quantum Theory and Symmetries, Valladolid, Spain, July 22-28,200

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

A q-analog of the ADHMN construction and axisymmetric multi-instantons

In the preceding paper (Phys. Lett. B463 (1999) 257), the authors presented a q-analog of the ADHMN construction and obtained a family of anti-selfdual configurations with a parameter q for classical SU(2) Yang-Mills theory in four-dimensional Euclidean space. The family of solutions can be seen as a q-analog of the single BPS monopole preserving (anti-)selfduality. Further discussion is made on the relation to axisymmetric ansatz on anti-selfdual equation given by Witten in the late seventies. It is found that the q-exponential functions familiar in q-analysis appear as analytic functions categorizing the anti-selfdual configurations yielded by axisymmetric ansatz.Comment: 11pages, Latex2e, to appear in Journal of Physics A: Mathematical and General as a `Special Issue/Difference Equations

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

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