Lie Superalgebra and Extended Topological Conformal Symmetry in Non-critical $W_3$ Strings

Abstract

We obtain a new free field realization of $N=2$ super $W_3$ algebra using the technique of quantum hamiltonian reduction. The construction is based on a particular choice of the simple root system of the affine Lie superalgebra $sl(3|2{)}^{(1)}$ associated with a non-standard $sl(2)$ embedding. After twisting and a similarity transformation, this $W$ algebra can be identified as the extended topological conformal algebra of non-critical $W_3$ string theory.

14pages, UTHEP-277

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