We study boundary value problems posed in a semistrip for the elliptic sine-Gordon equation, which is the paradigm of an elliptic integrable PDE in two variables. We use the method introduced by one of the authors, which provides a substantial generalization of the inverse scattering transform and can be used for the analysis of boundary as opposed to initial-value problems. We first express th...

The Bethe ansatz approach for factorizable centrally extended su(2|2) S-matrices Abstract We consider the Bethe ansatz solution of integrable models interacting through factor-ized S-matrices based on the central extention of the su(2|2) symmetry. The respective su(2|2) R-matrix is explicitly related to that of the covering Hubbard model through a spectral parameter dependent transformation. Th...

Maximally supersymmetric gauge theories have experienced renewed interest due to the AdS/CFT correspondence and its conjectured S-duality. These gauge theories possess a large amount of symmetry and have quasi-integrable properties. We derive the amplitudes in the derivative expansion of the spontaneously broken examples and perform all loop integrations. The S-matrix is found via an algebraic ...

We define an integrable lattice model which, in the notation of Yang, in addition to the conventional 2-particle R-matrices also contains non-reducible 3-particle R-matrices. The corresponding modified Yang-Baxter equations are solved and an expression for the transfer matrix is found as a normal ordered exponential of a (non-local) Hamiltonian. March 2004 e-mail:[email protected] e-mail:shah@...

Positive and negative hierarchies of non-isospectral multi-component AKNS equations are derived from an arbitrary order matrix spectral problem. Moreover, new non-isospectral multi-component integrable couplings of the resulting soliton hierarchies are constructed by enlarging the associated matrix spectral problem. Mathematics Subject Classification: 35Q58

A bstract This work concerns the quantum Lorentzian and Euclidean black hole non-linear sigma models. For model an equilibrium density matrix is proposed, which reproduces modular invariant partition function from 2001 paper of Maldacena, Ooguri Son. model, using its formulation as a gauged SL(2, ?) WZW we describe linear Hermitian structure space states also propose expression for matrix. Our ...