244 research outputs found
S-matrices of non-simply laced affine Toda theories by folding
The exact factorisable quantum S-matrices are known for simply laced as well
as non-simply laced affine Toda field theories. Non-simply laced theories are
obtained from the affine Toda theories based on simply laced algebras by
folding the corresponding Dynkin diagrams. The same process, called classical
`reduction', provides solutions of a non-simply laced theory from the classical
solutions with special symmetries of the parent simply laced theory. In the
present note we shall elevate the idea of folding and classical reduction to
the quantum level. To support our views we have made some interesting
observations for S-matrices of non-simply laced theories and give prescription
for obtaining them through the folding of simply laced ones.Comment: 26 pages, Latex2e, 4 figure
Exact S-Matrices for Bound States of Affine Toda Solitons
Using Hollowood's conjecture for the S-matrix for elementary solitons in
complex affine Toda field theories we examine the interactions of
bound states of solitons in theory. The elementary solitons can
form two different kinds of bound states: scalar bound states (the so-called
breathers), and excited solitons, which are bound states with non-zero
topological charge. We give explicit expressions of all S-matrix elements
involving the scattering of breathers and excited solitons and examine their
pole structure in detail. It is shown how the poles can be explained in terms
of on-shell diagrams, several of which involve a generalized Coleman-Thun
mechanism.Comment: Comments to figure 1 changed, some misprints corrected, 31 pages,
LATEX. (Version accepted for publication in NUCLEAR PHYSICS B
Toda Soliton Mass Corrections and the Particle--Soliton Duality Conjecture
We compute quantum corrections to soliton masses in affine Toda theories with
imaginary exponentials based on the nonsimply-laced Lie algebras .
We find that the soliton mass ratios renormalize nontrivially, in the same
manner as those of the fundamental particles of the theories with real
exponentials based on the nonsimply-laced algebras . This gives
evidence that the conjectured relation between solitons in one Toda theory and
fundamental particles in a dual Toda theory holds also at the quantum level.
This duality can be seen as a toy model for S-duality.Comment: LATEX, 17 pages, no figures Note added at end of discussio
Tau-Functions generating the Conservation Laws for Generalized Integrable Hierarchies of KdV and Affine-Toda type
For a class of generalized integrable hierarchies associated with affine
(twisted or untwisted) Kac-Moody algebras, an explicit representation of their
local conserved densities by means of a single scalar tau-function is deduced.
This tau-function acts as a partition function for the conserved densities,
which fits its potential interpretation as the effective action of some quantum
system. The class consists of multi-component generalizations of the
Drinfel'd-Sokolov and the two-dimensional affine Toda lattice hierarchies. The
relationship between the former and the approach of Feigin, Frenkel and
Enriquez to soliton equations of KdV and mKdV type is also discussed. These
results considerably simplify the calculation of the conserved charges carried
by the soliton solutions to the equations of the hierarchy, which is important
to establish their interpretation as particles. By way of illustration, we
calculate the charges carried by a set of constrained KP solitons recently
constructed.Comment: 47 pages, plain TeX with AMS fonts, no figure
Local conserved charges in principal chiral models
Local conserved charges in principal chiral models in 1+1 dimensions are
investigated. There is a classically conserved local charge for each totally
symmetric invariant tensor of the underlying group. These local charges are
shown to be in involution with the non-local Yangian charges. The Poisson
bracket algebra of the local charges is then studied. For each classical
algebra, an infinite set of local charges with spins equal to the exponents
modulo the Coxeter number is constructed, and it is shown that these commute
with one another. Brief comments are made on the evidence for, and implications
of, survival of these charges in the quantum theory.Comment: 36 pages, LaTeX; v2: minor correction
Exact S-Matrices with Affine Quantum Group Symmetry
We show how to construct the exact factorized S-matrices of 1+1 dimensional
quantum field theories whose symmetry charges generate a quantum affine
algebra. Quantum affine Toda theories are examples of such theories. We take
into account that the Lorentz spins of the symmetry charges determine the
gradation of the quantum affine algebras. This gives the S-matrices a non-rigid
pole structure. It depends on a kind of ``quantum'' dual Coxeter number which
will therefore also determine the quantum mass ratios in these theories. As an
example we explicitly construct S-matrices with symmetry.Comment: Latex file, 21 page
Integrable N=2 Supersymmetric Field Theories
Some additional references are included on the last 3 pages.Comment: 14 pages, OUTP-92-12
Exact S-matrices for d_{n+1}^{(2)} affine Toda solitons and their bound states
We conjecture an exact S-matrix for the scattering of solitons in
affine Toda field theory in terms of the R-matrix of the
quantum group . From this we construct the scattering
amplitudes for all scalar bound states (breathers) of the theory. This S-matrix
conjecture is justified by detailed examination of its pole structure. We show
that a breather-particle identification holds by comparing the S-matrix
elements for the lowest breathers with the S-matrix for the quantum particles
in real affine Toda field theory, and discuss the implications for various
forms of duality.Comment: Some minor changes and misprints corrected. Version to appear in
Nuclear Physics B, 40 pages, LATE
The Quantum Spectrum of the Conserved Charges in Affine Toda Theories
The exact eigenvalues of the infinite set of conserved charges on the
multi-particle states in affine Toda theories are determined. This is done by
constructing a free field realization of the Zamolodchikov-Faddeev algebra in
which the conserved charges are realized as derivative operators. The resulting
eigenvalues are renormalization group (RG) invariant, have the correct
classical limit and pass checks in first order perturbation theory. For
one recovers the (RG invariant form of the) quantum masses of Destri and
DeVega.Comment: 38p, 1 fig. included, MPI-Ph/93-92, LATE
Non-unitarity in quantum affine Toda theory and perturbed conformal field theory
There has been some debate about the validity of quantum affine Toda field
theory at imaginary coupling, owing to the non-unitarity of the action, and
consequently of its usefulness as a model of perturbed conformal field theory.
Drawing on our recent work, we investigate the two simplest affine Toda
theories for which this is an issue - a2(1) and a2(2). By investigating the
S-matrices of these theories before RSOS restriction, we show that quantum Toda
theory, (with or without RSOS restriction), indeed has some fundamental
problems, but that these problems are of two different sorts. For a2(1), the
scattering of solitons and breathers is flawed in both classical and quantum
theories, and RSOS restriction cannot solve this problem. For a2(2) however,
while there are no problems with breather-soliton scattering there are instead
difficulties with soliton-excited soliton scattering in the unrestricted
theory. After RSOS restriction, the problems with kink-excited kink may be
cured or may remain, depending in part on the choice of gradation, as we found
in [12]. We comment on the importance of regradations, and also on the survival
of R-matrix unitarity and the S-matrix bootstrap in these circumstances.Comment: 29 pp, LaTex2e, 6 eps and 1 ps figure
- …