W{1+ \infty} algebra, W_3 algebra, and Friedan-Martinec-Shenker bosonization

Details W{1+ \infty} algebra, W_3 algebra, and Friedan-Martinec-Shenker bosonization W{1+ \infty} algebra, W_3 algebra, and Friedan-Martinec-Shenker bosonization

1997-08-07

arxiv.org/abs/q-alg/9708008v1

Commun.Math.Phys. 195 (1998) 95-111

Physics

High Energy Physics

High Energy Physics - Theory

Latex, 23 pages

Scientific paper

10.1007/s002200050381

We show that the vertex algebra W{1+ \infty} with central charge -1 is isomorphic to a tensor product of the simple W_3 algebra with central charge -2 and a Heisenberg vertex algebra generated by a free bosonic field. We construct a family of irreducible modules of the W_3 algebra with central charge -2 in terms of free fields and calculate the full character formulas of these modules with respect to the full Cartan subalgebra of the W_3 algebra.

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