23 research outputs found
The Problem of Differential Calculus on Quantum Groups
The bicovariant differential calculi on quantum groups of Woronowicz have the
drawback that their dimensions do not agree with that of the corresponding
classical calculus. In this paper we discuss the first-order differential
calculus which arises from a simple quantum Lie algebra. This calculus has the
correct dimension and is shown to be bicovariant and complete. But it does not
satisfy the Leibniz rule. For sl_n this approach leads to a differential
calculus which satisfies a simple generalization of the Leibniz rule.Comment: Contribution to the proceedings of the Colloquium on Quantum Groups
and Integrable Systems Prague, June 1996. amslatex, 9 pages. For related
information see http://www.mth.kcl.ac.uk/~delius/q-lie.htm
Exact S-Matrices for Nonsimply-Laced Affine Toda Theories
We derive exact, factorized, purely elastic scattering matrices for affine
Toda theories based on the nonsimply-laced Lie algebras and superalgebras.Comment: 38 page
Exact s-Matrices for the Nonsimply-Laced Affine Toda Theories
We derive the exact, factorized, purely elastic scattering matrices for the
family of nonsimply-laced affine Toda theories. The derivation
takes into account the distortion of the classical mass spectrum by radiative
correction, as well as modifications of the usual bootstrap assumptions since
for these theories anomalous threshold singularities lead to a displacement of
some single particle poles.Comment: 11 page
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
Quantum Conserved Currents in Affine Toda Theories
We study the renormalization and conservation at the quantum level of
higher-spin currents in affine Toda theories with particular emphasis on the
nonsimply-laced cases. For specific examples, namely the spin-3 current for the
and theories, we prove conservation to all-loop order,
thus establishing the existence of factorized S-matrices. For these theories,
as well as the simply-laced theory, we compute one-loop corrections
to the corresponding higher-spin charges and study charge conservation for the
three-particle vertex function. For the theory we show that
although the current is conserved, anomalous threshold singularities spoil the
conservation of the corresponding charge for the on-shell vertex function,
implying a breakdown of some of the bootstrap procedures commonly used in
determining the exact S-matrix.Comment: 19 page
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
Induced (N,0) supergravity as a constrained Osp(N,2) WZWN model and its effective action
A chiral supergravity theory in d=2 dimensions for any and its
induced action can be obtained by constraining the currents of an Osp(N2)
WZWN model. The underlying symmetry algebras are the nonlinear SO(N)
superconformal algebras of Knizhnik and Bershadsky. The case is worked
out in detail. We show that by adding quantum corrections to the classical
transformation rules, the gauge algebra on gauge fields and currents closes.
Integrability conditions on Ward identities are derived. The effective action
is computed at one loop. It is finite, and can be obtained from the induced
action by rescaling the central charge and fields by finite Z factors.Comment: 23
Magnon Bound-state Scattering in Gauge and String Theory
It has been shown that, in the infinite length limit, the magnons of the
gauge theory spin chain can form bound states carrying one finite and one
strictly infinite R-charge. These bound states have been argued to be
associated to simple poles of the multi-particle scattering matrix and to world
sheet solitons carrying the same charges. Classically, they can be mapped to
the solitons of the complex sine-Gordon theory.
Under relatively general assumptions we derive the condition that simple
poles of the two-particle scattering matrix correspond to physical bound states
and construct higher bound states ``one magnon at a time''. We construct the
scattering matrix of the bound states of the BDS and the AFS S-matrices. The
bound state S-matrix exhibits simple and double poles and thus its analytic
structure is much richer than that of the elementary magnon S-matrix. We also
discuss the bound states appearing in larger sectors and their S-matrices. The
large 't Hooft coupling limit of the scattering phase of the bound states in
the SU(2) sector is found to agree with the semiclassical scattering of world
sheet solitons. Intriguingly, the contribution of the dressing phase has an
independent world sheet interpretation as the soliton-antisoliton scattering
phase shift. The small momentum limit provides independent tests of these
identifications.Comment: 25 pages, Latex V2: clarifying comments added to footnote 1 and
footnote 10; references added V3: typos correcte
Yangians, Integrable Quantum Systems and Dorey's rule
We study tensor products of fundamental representations of Yangians and show
that the fundamental quotients of such tensor products are given by Dorey's
rule.Comment: We have made corrections to the results for the Yangians associated
to the non--simply laced algebra
Holonomy groups and W-symmetries
Irreducible sigma models, i.e. those for which the partition function does
not factorise, are defined on Riemannian spaces with irreducible holonomy
groups. These special geometries are characterised by the existence of
covariantly constant forms which in turn give rise to symmetries of the
supersymmetric sigma model actions. The Poisson bracket algebra of the
corresponding currents is a W-algebra. Extended supersymmetries arise as
special cases.Comment: pages 2