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Author Bazhanov, Vladimir V. ♦ Hibberd, Anthony N. ♦ Khoroshkin, Sergey M.
Source arXiv.org
Content type Text
File Format PDF
Date of Submission 2001-05-18
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Natural sciences & mathematics ♦ Mathematics ♦ Physics
Subject Keyword High Energy Physics - Theory ♦ Condensed Matter ♦ Mathematical Physics ♦ Nonlinear Sciences - Exactly Solvable and Integrable Systems ♦ math ♦ nlin ♦ physics:cond-mat ♦ physics:hep-th ♦ physics:math-ph
Abstract In this paper we study the Yang-Baxter integrable structure of Conformal Field Theories with extended conformal symmetry generated by the W_3 algebra. We explicitly construct various T- and Q-operators which act in the irreducible highest weight modules of the W_3 algebra. These operators can be viewed as continuous field theory analogues of the commuting transfer matrices and Q-matrices of the integrable lattice systems associated with the quantum algebra U_q(\hat{sl}(3)). We formulate several conjectures detailing certain analytic characteristics of the Q-operators and propose exact asymptotic expansions of the T- and Q-operators at large values of the spectral parameter. We show, in particular, that the asymptotic expansion of the T-operators generates an infinite set of local integrals of motion of the W_3 CFT which in the classical limit reproduces an infinite set of conserved Hamiltonians associated with the classical Boussinesq equation. We further study the vacuum eigenvalues of the Q-operators (corresponding to the highest weight vector of the W_3 module) and show that they are simply related to the expectation values of the boundary exponential fields in the non-equilibrium boundary affine Toda field theory with zero bulk mass.
Description Reference: Nucl.Phys.B622:475-547,2002
Educational Use Research
Learning Resource Type Article
Page Count 87


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