Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rationality of Bershadsky-Polyakov vertex algebras   We prove the conjecture of Kac-Wakimoto on the rationality of exceptional
W-algebras for the first non-trivial series, namely, for the
Bershadsky-Polyakov vertex algebras $W_3^{(2)}$ at level $k=p/2-3$ with
$p=3,5,7,...$. This gives new examples of rational conformal field theories.

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The categories of this paper are: supr-con
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The categories of this paper are: mtrl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: math-ph
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The categories of this paper are: econ
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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: eess
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: astro-ph