A BRST Analysis of $W$-symmetries

Details A BRST Analysis of $W$-symmetries A BRST Analysis of $W$-symmetries

1993-07-07

arxiv.org/abs/hep-th/9307046v1

Nucl.Phys. B411 (1994) 717-744

Physics

High Energy Physics

High Energy Physics - Theory

32 pages, UG-4/93

Scientific paper

10.1016/0550-3213(94)90468-5

We perform a classical BRST analysis of the symmetries corresponding to a generic $w_N$-algebra. An essential feature of our method is that we write the $w_N$-algebra in a special basis such that the algebra manifestly has a ``nested'' set of subalgebras $v_N^N \subset v_N^{N-1} \subset \dots \subset v_N^2 \equiv w_N$ where the subalgebra $v_N^i\ (i=2, \dots ,N)$ consists of generators of spin $s=\{i,i+1,\dots ,N\}$, respectively. In the new basis the BRST charge can be written as a ``nested'' sum of $N-1$ nilpotent BRST charges. In view of potential applications to (critical and/or non-critical) $W$-string theories we discuss the quantum extension of our results. In particular, we present the quantum BRST-operator for the $W_4$-algebra in the new basis. For both critical and non-critical $W$-strings we apply our results to discuss the relation with minimal models.

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