We study the quantum integrability of nonsimply–laced affine Toda theories defined on the half–plane and explicitly construct the first nontrivial higher–spin charges in specific examples. We find that, in contradistinction to the classical case, addition of total derivative terms to the ”bulk” current plays a relevant role for the quantum boundary conservation. IFUM–518–FT October 1995 Two–dim...

Let G be a simply connected simple Lie group over C. Let N± be the positive and the negative maximal unipotent subgroups, and H the maximal torus, corresponding to some polarization of G. Let G0 = N−HN+ be the big Bruhat cell. Let χ± : N± → C be holomorphic nondegenerate characters (i.e. they don’t vanish on simple roots). A Whittaker function on G0 with characters χ+, χ− is any holomorphic fun...

An infinite class of fermionic flows of the N=(1|1) superconformal Toda lattice hierarchy is constructed and their algebraic structure is studied. We completely solve the semi-infinite N=(1|1) Toda lattice and chain hierarchies and derive their tau functions, which may be relevant for building supersymmetric matrix models. Their bosonic limit is also discussed. 1. Introduction. Recently the N=(...

FPU models, in dimension one, are perturbations either of the linear model or of the Toda model; perturbations of the linear model include the usual β-model, perturbations of Toda include the usual α+β model. In this paper we explore and compare two families, or hierarchies, of FPU models, closer and closer to either the linear or the Toda model, by computing numerically, for each model, the ma...

Some properties of the non-commutative versions of the sine-Gordon model (NCSG) and the corresponding massive Thirring theories (NCMT) are studied. Our method relies on the NC extension of integrable models and the master Lagrangian approach to deal with dual theories. The master Lagrangians turn out to be the NC versions of the so-called affine Toda model coupled to matter fields (NCATM) assoc...

A numerical and analytical study of the relaxation to equilibrium of both the Fermi-Pasta-Ulam (FPU) α-model and the integrable Toda model, when the fundamental mode is initially excited, is reported. We show that the dynamics of both systems is almost identical on the short term, when the energies of the initially unexcited modes grow in geometric progression with time, through a secular avala...

General properties of a class of two-dimensional dilaton gravity (DG) theories with multiexponential potentials are studied and a subclass of these theories, in which the equations of motion reduce to Toda and Liouville equations, is treated in detail. A combination of parameters of the equations should satisfy a certain constraint that is identified and solved for the general multi-exponential...

It is well-known that the partition function of the unitary ensembles of random matrices is given by a τ -function of the Toda lattice hierarchy and those of the orthogonal and symplectic ensembles are τ -functions of the Pfaff lattice hierarchy. In these cases the asymptotic expansions of the free energies given by the logarithm of the partition functions lead to the dispersionless (i.e. conti...

In this paper we construct global action-angle variables for the periodic Toda lattice.

We express the Poisson brackets of local fields of the affine Toda field theories in terms of the Drinfeld-Sokolov dressing operator. For this, we introduce a larger space of fields, containing “half screening charges” and “half integrals of motions”. In addition to local terms, the Poisson brackets contain nonlocal terms related to trigonometric r-matrices. Introduction Since the work of Zakha...