Integrable Quantum Field Theories with Unstable Particles

A new family of S-matrix theories with resonance poles is constructed and conjectured to correspond to the Homogeneous sine-Gordon theories associated with simply laced compact Lie groups, where some of the resonance poles can be traced to the presence of unstable particles in the spectrum. These theories are unitary in the usual S S^\dagger =1 sense, they are not parity invariant, and they exhibit continuous coupling constants that determine both the mass spectrum of stable particles and the masses and the position of the resonance poles.Comment: One reference added, 12 pages, LaTeX fil

Hermitian analyticity versus Real analyticity in two-dimensional factorised S-matrix theories

The constraints implied by analyticity in two-dimensional factorised S-matrix theories are reviewed. Whenever the theory is not time-reversal invariant, it is argued that the familiar condition of `Real analyticity' for the S-matrix amplitudes has to be superseded by a different one known as `Hermitian analyticity'. Examples are provided of integrable quantum field theories whose (diagonal) two-particle S-matrix amplitudes are Hermitian analytic but not Real analytic. It is also shown that Hermitian analyticity is consistent with the bootstrap equations and that it ensures the equivalence between the notion of unitarity in the quantum group approach to factorised S-matrices and the genuine unitarity of the S-matrix.Comment: 9 pages, LaTeX file. The comments about unitarity in affine Toda theories have been improved. The basis dependence of the Hermitian analyticity conditions is discusse

Massive symmetric space sine-Gordon soliton theories and perturbed conformal field theory

The perturbed conformal field theories corresponding to the massive Symmetric Space sine-Gordon soliton theories are identified by calculating the central charge of the unperturbed conformal field theory and the conformal dimension of the perturbation. They are described by an action with a positive-definite kinetic term and a real potential term bounded from below, their equations of motion are non-abelian affine Toda equations and, moreover, they exhibit a mass gap. The unperturbed CFT corresponding to the compact symmetric space G/G_0 is either the WZNW action for G_0 or the gauged WZNW action for a coset of the form G_0/U(1)^p. The quantum integrability of the theories that describe perturbations of a WZNW action, named Split models, is established by showing that they have quantum conserved quantities of spin +3 and -3. Together with the already known results for the other massive theories associated with the non-abelian affine Toda equations, the Homogeneous sine-Gordon theories, this supports the conjecture that all the massive Symmetric Space sine-Gordon theories will be quantum integrable and, hence, will admit a factorizable S-matrix. The general features of the soliton spectrum are discussed, and some explicit soliton solutions for the Split models are constructed. In general, the solitons will carry both topological charges and abelian Noether charges. Moreover, the spectrum is expected to include stable and unstable particles

Massive Integrable Soliton Theories

Massive integrable field theories in $1+1$ dimensions are defined at the Lagrangian level, whose classical equations of motion are related to the ``non-abelian'' Toda field equations. They can be thought of as generalizations of the sine-Gordon and complex sine-Gordon theories. The fields of the theories take values in a non-abelian Lie group and it is argued that the coupling constant is quantized, unlike the situation in the sine-Gordon theory, which is a special case since its field takes values in an abelian group. It is further shown that these theories correspond to perturbations of certain coset conformal field theories. The solitons in the theories will, in general, carry non-abelian charges.Comment: 18 pages, no figures, plain tex with macro include

Solitonic Integrable Perturbations of Parafermionic Theories

The quantum integrability of a class of massive perturbations of the parafermionic conformal field theories associated to compact Lie groups is established by showing that they have quantum conserved densities of scale dimension 2 and 3. These theories are integrable for any value of a continuous vector coupling constant, and they generalize the perturbation of the minimal parafermionic models by their first thermal operator. The classical equations-of-motion of these perturbed theories are the non-abelian affine Toda equations which admit (charged) soliton solutions whose semi-classical quantization is expected to permit the identification of the exact S-matrix of the theory.Comment: 18 pages, plain TeX, no figure

Solitons, Tau-functions and Hamiltonian Reduction for Non-Abelian Conformal Affine Toda Theories

We consider the Hamiltonian reduction of the two-loop Wess-Zumino-Novikov-Witten model (WZNW) based on an untwisted affine Kac-Moody algebra \cgh. The resulting reduced models, called {\em Generalized Non-Abelian Conformal Affine Toda (G-CAT)}, are conformally invariant and a wide class of them possesses soliton solutions; these models constitute non-abelian generalizations of the Conformal Affine Toda models. Their general solution is constructed by the Leznov-Saveliev method. Moreover, the dressing transformations leading to the solutions in the orbit of the vacuum are considered in detail, as well as the $\tau$-functions, which are defined for any integrable highest weight representation of \cgh, irrespectively of its particular realization. When the conformal symmetry is spontaneously broken, the G-CAT model becomes a generalized Affine Toda model, whose soliton solutions are constructed. Their masses are obtained exploring the spontaneous breakdown of the conformal symmetry, and their relation to the fundamental particle masses is discussed.Comment: 47 pages. LaTe

A T-duality interpretation of the relationship between massive and massless magnonic TBA systems.

We propose an alternative understanding of the relationship between massive and massless magnonic TBA systems, using the T-duality symmetries of the Homogeneous sine–Gordon models. This is shown to be in agreement with a previous treatment by Dorey, Dunning and Tateo, based on the properties of Y-systems