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arXiv · hep-th/9512160

A QFT approach to W_{1+infty}

B. N. Bakalov·L. S. Georgiev·I. T. Todorov
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Abstract

W_{1+infty} is defined as an infinite dimensional Lie algebra spanned by the unit operator and the Laurent modes of a series of local quasiprimary chiral fields V^l(z) of dimension l+1 (l=0,1,2,...). These fields are neutral with respect to the u(1) current J(z)=V^0(z); as a result the (l+2)-fold commutator of J with V^l vanishes. We outline a construction of rational conformal field theories with stress energy tensor T(z)=V^1(z) whose chiral algebras include all V^l's. It is pointed out that earlier work on local extensions of the u(1) current algebra solves the problem of classifying all such theories for Virasoro central charge c=1.

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B. N. Bakalov, L. S. Georgiev, I. T. Todorov. 1995-12-20. A QFT approach to W_{1+infty}. https://arxiv.org/abs/hep-th/9512160

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