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Permutation orbifolds of Virasoro vertex algebras and $W$-algebras (2005.08398v2)
Published 17 May 2020 in math.QA and math.RT
Abstract: We study permutation orbifolds of the $2$-fold and $3$-fold tensor product for the Virasoro vertex algebra $\mathcal{V}c$ of central charge $c$. In particular, we show that for all but finitely many central charges $\left(\mathcal{V}_c{\otimes 3}\right){\mathbb{Z}_3}$ is a $W$-algebra of type $(2, 4, 5, 63 , 7, 83 , 93 , 102 )$. We also study orbifolds of their simple quotients and obtain new realizations of certain rational affine $W$-algebras associated to a principal nilpotent element. Further analysis of permutation orbifolds of the celebrated $(2,5)$-minimal vertex algebra $\mathcal{L}{-\frac{22}{5}}$ is presented.