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Lie Superalgebra and Extended Topological Conformal Symmetry in Non-critical $W_{3}$ Strings

Katsushi Ito·Hiroaki Kanno
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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.

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Katsushi Ito, Hiroaki Kanno. 1994-05-09. Lie Superalgebra and Extended Topological Conformal Symmetry in Non-critical $W_{3}$ Strings. https://doi.org/10.1142/s0217732394002896

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