27 research outputs found
Quantum Inverse Scattering Method and (Super)Conformal Field Theory
In this paper we consider the possibility of application of the quantum
inverse scattering method for studying the superconformal field theory and it's
integrable perturbations. The classical limit of the considered constructions
is based on super-KdV hierarchy. The quantum counterpart of
the monodromy matrix corresponding to the linear problem associated with the
L-operator is introduced. Using the explicit form of the irreducible
representations of , the ``fusion relations'' for the
transfer-matrices (i.e. the traces of the monodromy matrices in different
representations) are obtained.Comment: LaTeX2e, 15 pages, Theor. Math. Phys., 2005, in pres
Group Theoretical Structure and Inverse Scattering Method for super-KdV Equation
Using the group-theoretical approach to the inverse scattering method the
supersymmetric Korteweg-de Vries equation is obtained by application of the
Drinfeld-Sokolov reduction to osp(1|2) loop superalgebra. The direct and
inverse scattering problems are discussed for the corresponding Lax pair.Comment: LaTeX2e, 19 pages, Zapiski Nauchnih Seminarov POMI (Steklov
Institute), vol. 291, 185-205, 2002 (in russian); Engl. transl. : Journal of
Math. Sci., Kluwer, in pres
Twisting adjoint module algebras
Transformation of operator algebras under Hopf algebra twist is studied. It
is shown that that adjoint module algebras are stable under the twist.
Applications to vector fields on non-commutative space-time are considered.Comment: 16 page
Integrable Structure of Superconformal Field Theory and Quantum super-KdV Theory
The integrable structure of the two dimensional superconformal field theory
is considered. The classical counterpart of our constructions is based on the
super-KdV hierarchy. The quantum version of the monodromy
matrix associated with the linear problem for the corresponding L-operator is
introduced. Using the explicit form of the irreducible representations of
, the so-called "fusion relations" for the transfer matrices
considered in different representations of are obtained. The
possible integrable perturbations of the model (primary operators, commuting
with integrals of motion) are classified and the relation with the
supersymmetric Toda field theory is discussed.Comment: LaTeX2e, elsart.cls, 11 pages, subm. to Physics Letters
Superconformal Field Theory and SUSY N=1 KdV Hierarchy II: The Q-operator
The algebraic structures related with integrable structure of superconformal
field theory (SCFT) are introduced. The SCFT counterparts of Baxter's
Q-operator are constructed. The fusion-like relations for the transfer-matrices
in different representations and their truncations are obtained.Comment: LaTeX2e, elsart.cls, 17 pages, Nuclear Physics B, 2005, in pres
Superconformal Field Theory and SUSY N=1 KdV Hierarchy I: Vertex Operators and Yang-Baxter Equation
The supersymmetry invariant integrable structure of two-dimensional
superconformal field theory is considered. The classical limit of the
corresponding infinite family of integrals of motion (IM) coincide with the
family of IM of SUSY N=1 KdV hierarchy. The quantum version of the monodromy
matrix, generating quantum IM, associated with the SUSY N=1 KdV is constructed
via vertex operator representation of the quantum R-matrix. The possible
applications to the perturbed superconformal models are discussed.Comment: LaTeX2e, elsart.cls, 11 pages, subm. to Physics Letters