Unitary Representations of $W$ Infinity Algebras

Details Unitary Representations of $W$ Infinity Algebras Unitary Representations of $W$ Infinity Algebras

1991-11-28

arxiv.org/abs/hep-th/9111058v1

Int.J.Mod.Phys. A7 (1992) 6339-6356

Physics

High Energy Physics

High Energy Physics - Theory

20 pages

Scientific paper

10.1142/S0217751X9200288X

We study the irreducible unitary highest weight representations, which are obtained from free field realizations, of $W$ infinity algebras ($W_{\infty}$, $W_{1+\infty}$, $W_{\infty}^{1,1}$, $W_{\infty}^M$, $W_{1+\infty}^N$, $W_{\infty}^{M,N}$) with central charges ($2$, $1$, $3$, $2M$, $N$, $2M+N$). The characters of these representations are computed. We construct a new extended superalgebra $W_{\infty}^{M,N}$, whose bosonic sector is $W_{\infty}^M\oplus W_{1+\infty}^N$. Its representations obtained from a free field realization with central charge $2M+N$, are classified into two classes: continuous series and discrete series. For the former there exists a supersymmetry, but for the latter a supersymmetry exists only for $M=N$.

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