17 research outputs found
On holomorphic factorization of two-dimensional gravity action
We solve the integrability conditions for the local covariant formulation of the induced action of 2d-gravity and propose gauge conditions under which the chiral fermion action is an expansion of the Polyakov action in the case when both functions f^± are retained
Heisenberg spin chains based on sl(2|1) symmetry
We find solutions of the Yang-Baxter equation acting on tensor product of
arbitrary representations of the superalgebra sl(2|1). Based on these solutions
we construct the local Hamiltonians for integrable homogeneous periodic chains
and open chains.Comment: 28 pages LATE
Universal R-matrix as integral operator
We derive the integral operator form for the general rational solution of the
Yang-Baxter equation with symmetry. Considering the defining
relations for the kernel of the R-operator as a system of second order
differential equations we observe remarkable reduction to a system of simple
first order equations. The obtained kernel of R-operator has a very simple
structure. To illustrate all this in the simplest situation we treat also the
case.Comment: 26 pages LaTe
Consistency conditions and trace anomalies in six dimensions
Conformally invariant quantum field theories develop trace anomalies when
defined on curved backgrounds. We study again the problem of identifying all
possible trace anomalies in d=6 by studying the consistency conditions to
derive their 10 independent solutions. It is known that only 4 of these
solutions represent true anomalies, classified as one type A anomaly, given by
the topological Euler density, and three type B anomalies, made up by three
independent Weyl invariants. However, we also present the explicit expressions
of the remaining 6 trivial anomalies, namely those that can be obtained by the
Weyl variation of local functionals. The knowledge of the latter is in general
necessary to disentangle the universal coefficients of the type A and B
anomalies from calculations performed on concrete models.Comment: 16 pages, LaTe
Universal R operator with deformed conformal symmetry
We study the general solution of the Yang-Baxter equation with deformed
symmetry. The universal R operator acting on tensor products of
arbitrary representations is obtained in spectral decomposition and in integral
forms. The results for eigenvalues, eigenfunctions and integral kernel appear
as deformations of the ones in the rational case. They provide a basis for the
construction of integrable quantum systems generalizing the XXZ spin models to
the case of arbitrary not necessarily finite-dimensional representations on the
sites.Comment: 18 pages LaTex, revised, to be publ. in Nucl. Phy
Baxter Q-operator and Separation of Variables for the open SL(2,R) spin chain
We construct the Baxter Q-operator and the representation of the Separated
Variables (SoV) for the homogeneous open SL(2,R) spin chain. Applying the
diagrammatical approach, we calculate Sklyanin's integration measure in the
separated variables and obtain the solution to the spectral problem for the
model in terms of the eigenvalues of the Q-operator. We show that the
transition kernel to the SoV representation is factorized into the product of
certain operators each depending on a single separated variable. As a
consequence, it has a universal pyramid-like form that has been already
observed for various quantum integrable models such as periodic Toda chain,
closed SL(2,R) and SL(2,C) spin chains.Comment: 29 pages, 9 figures, Latex styl
Nemrut Caldera and Eastern Anatolian Volcanoes: Fire in the Highlands
International audienc