Rationality of Bershadsky-Polyakov vertex algebras
Tomoyuki Arakawa

TL;DR
This paper proves the rationality of Bershadsky-Polyakov vertex algebras at specific levels, providing new examples of rational conformal field theories and confirming a conjecture by Kac-Wakimoto.
Contribution
It confirms the Kac-Wakimoto conjecture for the first non-trivial series of exceptional W-algebras, specifically for Bershadsky-Polyakov algebras at certain levels.
Findings
Proves rationality of $W_3^{(2)}$ at levels $k=p/2-3$ for $p=3,5,7,...$
Provides new examples of rational conformal field theories
Validates the Kac-Wakimoto conjecture for these algebras
Abstract
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 at level with . This gives new examples of rational conformal field theories.
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