Rational vs Polynomial Character of W$_n^l$-Algebras

L. Feher; L. O'Raifeartaigh; P. Ruelle; I. Tsutsui

doi:10.1016/0370-2693(92)90015-V

paper

Rational vs Polynomial Character of W $_{n}^{l}$ -Algebras

arXiv:hep-th/9201038 · doi:10.1016/0370-2693(92)90015-V

Abstract

The constraints proposed recently by Bershadsky to produce $W_{n}^{l}$ algebras are a mixture of first and second class constraints and are degenerate. We show that they admit a first-class subsystem from which they can be recovered by gauge-fixing, and that the non-degenerate constraints can be handled by previous methods. The degenerate constraints present a new situation in which the natural primary field basis for the gauge-invariants is rational rather than polynomial. We give an algorithm for constructing the rational basis and converting the base elements to polynomials.

18 pages

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Rational vs Polynomial Character of W $_{n}^{l}$ -Algebras