English

On the KP Hierarchy, $\hat{W}_{\infty}$ Algebra, and Conformal SL(2,R)/U(1) Model: II. The Quantum Case

High Energy Physics - Theory 2009-10-22 v1

Abstract

This paper is devoted to constructing a quantum version of the famous KP hierarchy, by deforming its second Hamiltonian structure, namely the nonlinear W^\hat{W}_{\infty} algebra. This is achieved by quantizing the conformal noncompact SL(2,R)k/U(1)SL(2,R)_{k}/U(1) coset model, in which W^\hat{W}_{\infty} appears as a hidden current algebra. For the quantum W^\hat{W}_{\infty} algebra at level k=1k=1, we have succeeded in constructing an infinite set of commuting quantum charges in explicit and closed form. Using them a completely integrable quantum KP hierarchy is constructed in the Hamiltonian form. A two boson realization of the quantum W^\hat{W}_{\infty} currents has played a crucial role in this exploration.

Keywords

Cite

@article{arxiv.hep-th/9210118,
  title  = {On the KP Hierarchy, $\hat{W}_{\infty}$ Algebra, and Conformal SL(2,R)/U(1) Model: II. The Quantum Case},
  author = {Feng Yu and Yong-Shi Wu},
  journal= {arXiv preprint arXiv:hep-th/9210118},
  year   = {2009}
}

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