A QFT approach to W_{1+infty}

TL;DR

This paper explores the structure of the W_{1+infty} algebra using quantum field theory methods, constructing related rational conformal field theories and connecting to known classifications at central charge c=1.

Contribution

It introduces a QFT approach to analyze W_{1+infty} and constructs rational conformal field theories with extended chiral algebras including all V^l fields.

Findings

W_{1+infty} algebra characterized by local quasiprimary fields

Construction of rational CFTs with stress tensor T(z)=V^1(z)

Connection to classification of theories at c=1

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.