Recent developments in affine Toda quantum field theory’, CRMCAP Summer School on Particles and (original) (raw)

Point symmetries of generalized Toda field theories: II. Symmetry reduction

Journal of Physics A: Mathematical and General, 2000

A class of two-dimensional field theories with exponential interactions is introduced. The interaction depends on two "coupling" matrices and is sufficiently general to include all Toda field theories existing in the literature. Lie point symmetries of these theories are found for an infinite, semi-infinite and finite number of fields. Special attention is accorded to conformal invariance and its breaking.

The Conserved Charges and Integrability of the Conformal Affine Toda Models

Modern Physics Letters A, 1994

We construct infinite sets of local conserved charges for the conformal affine Toda model. The technique involves the abelianization of the two-dimensional gauge potentials satisfying the zero-curvature form of the equations of motion. We find two infinite sets of chiral charges and apart from two lowest spin charges, all the remaining ones do not possess chiral densities. Charges of different chiralities Poisson commute among themselves. We discuss the algebraic properties of these charges and use the fundamental Poisson bracket relation to show that the charges conserved in time are in involution. Connections to other Toda models are established by taking particular limits.

Extended C = ∞ conformal systems from classical toda field theories

Nuclear Physics B, 1989

In a recent article we showed that the bosonic Toda field theories obey extended Virasoro symmetries which involve generators of spins higher than two; and that their quantization gives a systematic treatment of generalized conformal bosonic models. Their Virasoro central charges are such that they become infinite in the classical limit. This latter situation is studied in detail in the present paper, where a simple form of the general solution of the Toda field equations is given, that allows one to separate the modes and to study the Poisson bracket structure of the generators of the extended symmetry in a systematic way. Besides its relevance to the study of integrable classical systems this paves the way to the quantum case, already discussed by the authors and to be worked out in full detail in a separate publication.

Multiple poles and other features of affine Toda field theory

Nuclear Physics B - NUCL PHYS B, 1991

Some perturbative features of affine Toda field theory are explored, in particular the mechanisms responsible for the first-, second-and third-order poles in the conjectured exact factorisable S-matrices in the ADE series of models. It is found that generic collections of Feynman diagrams are responsible for the leading order poles in any of the theories. However, the complexity is such that it has not yet proved possible to analyse all the singularities that occur up to order twelve. Some comments are made on an associated tiling problem and on an interesting connection between the affine Toda couplings and the Clebsch-Gordan decomposition of tensor products .

The S-matrix coupling dependence for a, d and e affine Toda field theory

Physics Letters B, 1991

Toda field theories are solvable 1 + 1 dimensional quantum field theories closely related to integrable deformations of conformal field theory. The S-matrix elements for an affine Toda field theory are believed to depend on the coupling constant fl through one universal function B(fl) which cannot be determined by unitarity, crossing and the bootstrap. From the requirement of nonexistence of extra poles in the physical region its form is conjectured to be B(fl)= (2~t)-lfl:/(1 + f12/4/t). We show that the above conjecture is correct up to one-loop order (i.e., f14) of perturbation for simply laced, i.e., a, d and e affine Toda field theories using a general argument which exhibits much of the richness of these theories.

Aspects of Affine Toda Field Theory on a Half Line

Progress of Theoretical Physics Supplement, 1995

The question of the integrability of real-coupling ane toda eld theory on a half line is discussed. It is shown, by examining low-spin conserved charges, that the boundary conditions preserving integrability are strongly constrained. In particular, among the cases treated so far, e 1

Conformal affine sl2 Toda field theory

Physics Letters B, 1990

We present a model based on the ~2 affine algebra, which is integrable and conformally invariant. It reduces to the standard Liouville theory or to the sinh-Gordon model under certain limiting conditions. We find the general classical solution of this model and the exchange algebra.

Conservation Laws for the Classical Toda Field Theories

Modern Physics Letters A, 1993

Some explicit calculations of the conservation laws for classical (affine) Toda field theories, and some generlizations of these models are performed. We show that there is a huge class of generalized models which have an infinite set of conservation laws, with their integrated charges being in involution. Amongst these models we find that only the Am, and [Formula: see text] Toda field theories admit such conservation laws for spin-3. The explicit calculations of spin-4 and spin-5 conservation laws in the (affine) Toda models we presented. Our perhaps most interesting finding is that there exist conservation laws in the Am, models (m≥4) which have a different origin than the exponents of the corresponding affine theory or the energy-momentum tensor of a conformal theory.