2,601 research outputs found

    Integrability of Superconformal Field Theory and SUSY N=1 KdV

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    The quantum SUSY N=1 hierarchy based on sl(2‚ą£1)(2)sl(2|1)^{(2)} twisted affine superalgebra is considered. The construction of the corresponding Baxter's Q-operators and fusion relations is outlined. The relation with the superconformal field theory is discussed.Comment: LaTeX2e, cargese.cls, 4 pages, Subm. to String Theory: from Gauge Interactions to Cosmology, NATO Advanced Study Institute, Proc. of Cargese Summer School, NATO Science series C, 200

    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

    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

    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^(1‚ą£2)\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(1‚ą£2)\hat{osp}_q(1|2), the so-called "fusion relations" for the transfer matrices considered in different representations of osp^q(1‚ą£2)\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^(1‚ą£2)\hat{osp}(1|2) Toda field theory is discussed.Comment: LaTeX2e, elsart.cls, 11 pages, subm. to Physics Letters

    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

    On integrable Hamiltonians for higher spin XXZ chain

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    Integrable Hamiltonians for higher spin periodic XXZ chains are constructed in terms of the spin generators; explicit examples for spins up to 3/2 are given. Relations between Hamiltonians for some U_q(sl_2)-symmetric and U(1)-symmetric universal r-matrices are studied; their properties are investigated. A certain modification of the higher spin periodic chain Hamiltonian is shown to be an integrable U_q(sl_2)-symmetric Hamiltonian for an open chain.Comment: 20 pages, Latex; Section 8 has been modifie
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