1,075 research outputs found

    Superconformal Field Theory and SUSY N=1 KdV Hierarchy II: The Q-operator

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    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

    Integrable Structure of Superconformal Field Theory and Quantum super-KdV Theory

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    The integrable structure of the two dimensional superconformal field theory is considered. The classical counterpart of our constructions is based on the osp^(12)\hat{osp}(1|2) 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 osp^q(12)\hat{osp}_q(1|2), the so-called "fusion relations" for the transfer matrices considered in different representations of osp^q(12)\hat{osp}_q(1|2) are obtained. The possible integrable perturbations of the model (primary operators, commuting with integrals of motion) are classified and the relation with the supersymmetric osp^(12)\hat{osp}(1|2) Toda field theory is discussed.Comment: LaTeX2e, elsart.cls, 11 pages, subm. to Physics Letters

    Quantum Supersymmetric Toda-mKdV Hierarchies

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    In this paper we generalize the quantization procedure of Toda-mKdV hierarchies to the case of arbitrary affine (super)algebras. The quantum analogue of the monodromy matrix, related to the universal R-matrix with the lower Borel subalgebra represented by the corresponding vertex operators is introduced. The auxiliary L-operators satisfying RTT-relation are constructed and the quantum integrability condition is obtained. General approach is illustrated by means of two important examples.Comment: LaTeX2e, elsart.cls, 21 pages, Nuclear Physics B, 2005, in pres

    Superconformal Field Theory and SUSY N=1 KdV Hierarchy I: Vertex Operators and Yang-Baxter Equation

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    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

    Twisting adjoint module algebras

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    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

    Quantum group covariant systems

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    The meaning of quantum group transformation properties is discussed in some detail by comparing the (co)actions of the quantum group with those of the corresponding Lie group, both of which have the same algebraic (matrix) form of the transformation. Various algebras are considered which are covariant with respect to the quantum (super) groups SUq(2),  SUq(1,1),  SUq(11),  SUq(n),SUq(mn),  OSpq(12)SU_q(2),\; SU_q(1, 1),\; SU_q(1|1),\; SU_q(n), \\ SU_q(m|n),\; OSp_q(1|2) as well as deformed Minkowski space-time algebras.Comment: 12 pages, Late

    Quantum Inverse Scattering Method and (Super)Conformal Field Theory

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    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 osp^(12)\hat{osp}(1|2) 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 osp^q(12)\hat{osp}_q(1|2), 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

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    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

    Reflection equations and q-Minkowski space algebras

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    We express the defining relations of the qq-deformed Minkowski space algebra as well as that of the corresponding derivatives and differentials in the form of reflection equations. This formulation encompasses the covariance properties with respect the quantum Lorentz group action in a straightforward way.Comment: 10 page
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