W1+ ∞ algebra, W3 algebra, and Friedan-Martinec-Shenker bosonization
Abstract
We show that the vertex algebra W1+ ∞ with central charge -1 is isomorphic to a tensor product of the simple W3 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 W3 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 W3 algebra.
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