997 research outputs found

### Trigonometric Degeneration and Orbifold Wess-Zumino-Witten Model. I

Trigonometric degeneration of the Baxter-Belavin elliptic r matrix is
described by the degeneration of the twisted WZW model on elliptic curves. The
spaces of conformal blocks and conformal coinvariants of the degenerate model
are factorised into those of the orbifold WZW model.Comment: 24 pages, 1 figure, contribution to ``Conformal Field Theory and
Integrable Models'', Chernogolovka, Moscow Region, Russia, on September
15--21, 2002; typos corrected, references added (v2); typos corrected, final
version (v3

### The 19-Vertex Model at critical regime $|q|=1$

We study the 19-vertex model associated with the quantum group
$U_q(\hat{sl_2})$ at critical regime $|q|=1$. We give the realizations of the
type-I vertex operators in terms of free bosons and free fermions. Using these
free field realizations, we give the integral representations for the
correlation functions.Comment: LaTEX2e, 19page

### A system of difference equations with elliptic coefficients and Bethe vectors

An elliptic analogue of the $q$ deformed Knizhnik-Zamolodchikov equations is
introduced. A solution is given in the form of a Jackson-type integral of Bethe
vectors of the XYZ-type spin chains.Comment: 20 pages, AMS-LaTeX ver.1.1 (amssymb), 15 figures in LaTeX picture
environment

### Knizhnik-Zamolodchikov-Bernard equations connected with the eight-vertex model

Using quasiclassical limit of Baxter's 8 - vertex R - matrix, an elliptic
generalization of the Knizhnik-Zamolodchikov equation is constructed. Via
Off-Shell Bethe ansatz an integrable representation for this equation is
obtained. It is shown that there exists a gauge transformation connecting this
equation with Knizhnik-Zamolodchikov-Bernard equation for SU(2)-WZNW model on
torus.Comment: 20 pages latex, macro: tcilate

### From finite geometry exact quantities to (elliptic) scattering amplitudes for spin chains: the 1/2-XYZ

Initially, we derive a nonlinear integral equation for the vacuum counting
function of the spin 1/2-XYZ chain in the {\it disordered regime}, thus
paralleling similar results by Kl\"umper \cite{KLU}, achieved through a
different technique in the {\it antiferroelectric regime}. In terms of the
counting function we obtain the usual physical quantities, like the energy and
the transfer matrix (eigenvalues). Then, we introduce a double scaling limit
which appears to describe the sine-Gordon theory on cylindrical geometry, so
generalising famous results in the plane by Luther \cite{LUT} and Johnson et
al. \cite{JKM}. Furthermore, after extending the nonlinear integral equation to
excitations, we derive scattering amplitudes involving solitons/antisolitons
first, and bound states later. The latter case comes out as manifestly related
to the Deformed Virasoro Algebra of Shiraishi et al. \cite{SKAO}. Although this
nonlinear integral equations framework was contrived to deal with finite
geometries, we prove it to be effective for discovering or rediscovering
S-matrices. As a particular example, we prove that this unique model furnishes
explicitly two S-matrices, proposed respectively by Zamolodchikov \cite{ZAMe}
and Lukyanov-Mussardo-Penati \cite{LUK, MP} as plausible scattering description
of unknown integrable field theories.Comment: Article, 41 pages, Late

### Construction of some missing eigenvectors of the XYZ spin chain at the discrete coupling constants and the exponentially large spectral degeneracy of the transfer matrix

We discuss an algebraic method for constructing eigenvectors of the transfer
matrix of the eight vertex model at the discrete coupling parameters. We
consider the algebraic Bethe ansatz of the elliptic quantum group $E_{\tau,
\eta}(sl_2)$ for the case where the parameter $\eta$ satisfies $2 N \eta = m_1
+ m_2 \tau$ for arbitrary integers $N$, $m_1$ and $m_2$. When $m_1$ or $m_2$
is odd, the eigenvectors thus obtained have not been discussed previously.
Furthermore, we construct a family of degenerate eigenvectors of the XYZ spin
chain, some of which are shown to be related to the $sl_2$ loop algebra
symmetry of the XXZ spin chain. We show that the dimension of some degenerate
eigenspace of the XYZ spin chain on $L$ sites is given by $N 2^{L/N}$, if $L/N$
is an even integer. The construction of eigenvectors of the transfer matrices
of some related IRF models is also discussed.Comment: 19 pages, no figure (revisd version with three appendices

### Coupled Modified KP Hierarchy and Its Dispersionless Limit

We define the coupled modified KP hierarchy and its dispersionless limit. This integrable hierarchy is a generalization of the ''half'' of the Toda lattice hierarchy as well as an extension of the mKP hierarchy. The solutions are parametrized by a fibered flag manifold. The dispersionless counterpart interpolates several versions of dispersionless mKP hierarchy

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