## 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}(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 nonequilibrium boundary affine Toda field theory with zero bulk mass.

Original language | English |
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Pages (from-to) | 475-547 |

Number of pages | 73 |

Journal | Nuclear Physics B |

Volume | 622 |

Issue number | 3 |

DOIs | |

Publication status | Published - 11 Feb 2002 |

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