3,958 research outputs found
Yang-Baxter equation, parameter permutations, and the elliptic beta integral
We construct an infinite-dimensional solution of the Yang-Baxter equation
(YBE) of rank 1 which is represented as an integral operator with an elliptic
hypergeometric kernel acting in the space of functions of two complex
variables. This R-operator intertwines the product of two standard L-operators
associated with the Sklyanin algebra, an elliptic deformation of sl(2)-algebra.
It is built from three basic operators , and
generating the permutation group of four parameters
. Validity of the key Coxeter relations (including the
star-triangle relation) is based on the elliptic beta integral evaluation
formula and the Bailey lemma associated with an elliptic Fourier
transformation. The operators are determined uniquely with the
help of the elliptic modular double.Comment: 43 pp., to appear in Russian Math. Survey
Finite-dimensional representations of the elliptic modular double
We investigate the kernel space of an integral operator M(g) depending on the
"spin" g and describing an elliptic Fourier transformation. The operator M(g)
is an intertwiner for the elliptic modular double formed from a pair of
Sklyanin algebras with the parameters and , Im,
Im. For two-dimensional lattices and with incommensurate and integers , the operator
M(g) has a finite-dimensional kernel that consists of the products of theta
functions with two different modular parameters and is invariant under the
action of generators of the elliptic modular double.Comment: 25 pp., published versio
Meromorphic Solutions to a Differential--Difference Equation Describing Certain Self-Similar Potentials
In this paper we prove the existence of meromorphic solutions to a nonlinear
differential difference equation that describe certain self-similar potentials
for the Schroedinger operator.Comment: 10 pages, LaTeX, uses additional package
Superconformal indices of three-dimensional theories related by mirror symmetry
Recently, Kim and Imamura and Yokoyama derived an exact formula for
superconformal indices in three-dimensional field theories. Using their
results, we prove analytically the equality of superconformal indices in some
U(1)-gauge group theories related by the mirror symmetry. The proofs are based
on the well known identities of the theory of -special functions. We also
suggest the general index formula taking into account the global
symmetry present for abelian theories.Comment: 17 pages; minor change
New elliptic solutions of the Yang-Baxter equation
We consider finite-dimensional reductions of an integral operator with the
elliptic hypergeometric kernel describing the most general known solution of
the Yang-Baxter equation with a rank 1 symmetry algebra. The reduced
R-operators reproduce at their bottom the standard Baxter's R-matrix for the
8-vertex model and Sklyanin's L-operator. The general formula has a remarkably
compact form and yields new elliptic solutions of the Yang-Baxter equation
based on the finite-dimensional representations of the elliptic modular double.
The same result is also derived using the fusion formalism.Comment: 34 pages, to appear in Commun. Math. Phy
Driving Operators Relevant: A Feature of Chern-Simons Interaction
By computing anomalous dimensions of gauge invariant composite operators
and in Chern-Simons fermion and boson
models, we address that Chern-Simons interactions make these operators more
relevant or less irrelevant in the low energy region. We obtain a critical
Chern-Simons fermion coupling, , for a phase
transition at which the leading irrelevant four-fermion operator
becomes marginal, and a critical Chern-Simons boson
coupling, , for a similar phase transition
for the leading irrelevant operator . We see this phenomenon
also in the expansion.Comment: (ten pages, latex, figures included
On a modular property of N=2 superconformal theories in four dimensions
In this note we discuss several properties of the Schur index of N=2
superconformal theories in four dimensions. In particular, we study modular
properties of this index under SL(2,Z) transformations of its parameters.Comment: 23 page, 2 figure
Loss of spiritual and moral values
В работе была рассмотрена проблема духовно-нравственного воспитания молодежи Российского общества. В процессе изучения были выявлены проблемы, которые были связаны с утратой духовных и нравственных ценностей, перед нами стояла задача выявить пути и методы решения этой проблемы.In this study we consider the problem of spiritual and moral education of the youth of the Russian society. In the course of studying the problems were identified that were associated with the loss of spiritual and moral values, our task was to identify ways and means of solving this problem
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