Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Cohomology of the Noncritical $W$-string   We investigate the cohomology structure of a general noncritical
$W_N$-string. We do this by introducing a new basis in the Hilbert space in
which the BRST operator splits into a ``nested'' sum of nilpotent BRST
operators. We give explicit details for the case $N=3$. In that case the BRST
operator $Q$ can be written as the sum of two, mutually anticommuting,
nilpotent BRST operators: $Q=Q_0+Q_1$. We argue that if one chooses for the
Liouville sector a $(p,q)$ $W_3$ minimal model then the cohomology of the $Q_1$
operator is closely related to a $(p,q)$ Virasoro minimal model. In particular,
the special case of a (4,3) unitary $W_3$ minimal model with central charge
$c=0$ leads to a $c=1/2$ Ising model in the $Q_1$ cohomology. Despite all this,
noncritical $W_3$ strings are not identical to noncritical Virasoro strings.

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The categories of this paper are: astro-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: math
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The categories of this paper are: hep-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: q-fin
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The categories of this paper are: acc-phys
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The categories of this paper are: ao-sci
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ph
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The categories of this paper are: eess
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The categories of this paper are: cs
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The categories of this paper are: funct-an
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The categories of this paper are: dg-ga
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The categories of this paper are: quant-ph
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The categories of this paper are: nlin