227 research outputs found
Lattice quantization of Yangian charges
By placing theories with Yangian charges on the lattice in the analogue of
the St Petersburg school's approach to the sine-Gordon system, we exhibit the
Yangian structure of the auxiliary algebra, and explain how the two Yangians
are related.Comment: 9 pages, LaTeX. v2 has minor changes, including correction of a
propagating sign erro
Classically integrable boundary conditions for symmetric-space sigma models
We investigate boundary conditions for the nonlinear sigma model on the
compact symmetric space , where is the subgroup fixed by an
involution of . The Poisson brackets and the classical local
conserved charges necessary for integrability are preserved by boundary
conditions in correspondence with involutions which commute with .
Applied to , the nonlinear sigma model on , these yield the
great circles as boundary submanifolds. Applied to , they
reproduce known results for the principal chiral model.Comment: 8 pages. v2 has an introduction added and a few minor correction
Twisted algebra R-matrices and S-matrices for affine Toda solitons and their bound states
We construct new and invariant
-matrices and comment on the general construction of -matrices for
twisted algebras. We use the former to construct -matrices for
affine Toda solitons and their bound states, identifying the lowest breathers
with the particles.Comment: Latex, 24 pages. Various misprints corrected. New section added
clarifying relationship between R-matrices and S-matrice
Remarks on excited states of affine Toda solitons
The identification in affine Toda field theory of the quantum particle with
the lowest breather allows us to re-interpret discrete modes of excitation of
solitons as breathers bound to solitons, and thus to investigate them through
the proposed soliton-breather S-matrices. There are implications for the
physical spectrum and for the semiclassical soliton mass corrections.Comment: 8pp, LaTeX. Comments and one reference added; version to appear in
Phys.Lett.
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
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
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
Quantum mass corrections for affine Toda solitons
We calculate the first quantum corrections to the masses of solitons in
imaginary-coupling affine Toda theories using the semi-classical method of
Dashen, Hasslacher and Neveu. The theories divide naturally into those based on
the simply-laced, the twisted and the untwisted non-simply-laced algebras. We
find that the classical relationships between soliton and particle masses found
by Olive {\em et al.\ }persist for the first two classes, but do not appear to
do so naively for the third.Comment: 39pp, .uu compressed dvifile. Revised version alters two references
and includes hep-th no. on Title pag
Conserved charges and supersymmetry in principal chiral and WZW models
Conserved and commuting charges are investigated in both bosonic and
supersymmetric classical chiral models, with and without Wess-Zumino terms. In
the bosonic theories, there are conserved currents based on symmetric invariant
tensors of the underlying algebra, and the construction of infinitely many
commuting charges, with spins equal to the exponents of the algebra modulo its
Coxeter number, can be carried out irrespective of the coefficient of the
Wess-Zumino term. In the supersymmetric models, a different pattern of
conserved quantities emerges, based on antisymmetric invariant tensors. The
current algebra is much more complicated than in the bosonic case, and it is
analysed in some detail. Two families of commuting charges can be constructed,
each with finitely many members whose spins are exactly the exponents of the
algebra (with no repetition modulo the Coxeter number). The conserved
quantities in the bosonic and supersymmetric theories are only indirectly
related, except for the special case of the WZW model and its supersymmetric
extension.Comment: LaTeX; 49 pages; v2: minor changes and additions to text and ref
Solitons and Vertex Operators in Twisted Affine Toda Field Theories
Affine Toda field theories in two dimensions constitute families of
integrable, relativistically invariant field theories in correspondence with
the affine Kac-Moody algebras. The particles which are the quantum excitations
of the fields display interesting patterns in their masses and coupling and
which have recently been shown to extend to the classical soliton solutions
arising when the couplings are imaginary. Here these results are extended from
the untwisted to the twisted algebras. The new soliton solutions and their
masses are found by a folding procedure which can be applied to the affine
Kac-Moody algebras themselves to provide new insights into their structures.
The relevant foldings are related to inner automorphisms of the associated
finite dimensional Lie group which are calculated explicitly and related to
what is known as the twisted Coxeter element. The fact that the twisted affine
Kac-Moody algebras possess vertex operator constructions emerges naturally and
is relevant to the soliton solutions.Comment: 27 pages (harvmac) + 3 figures (LaTex) at the end of the file,
Swansea SWAT/93-94/1
- âŠ