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arXiv · 2209.13341

$S_3$-Permutation Orbifolds of Virasoro Vertex Algebras

Antun Milas·Michael Penn·Christopher Sadowski
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Abstract

In this paper, a continuation of \cite{MPS}, we investigate the $S_3$-orbifold subalgebra of $(\mathcal{V}_c)^{\otimes 3}$, that is, we consider the $S_3$-fixed point vertex subalgebra of the tensor product of three copies of the universal Virasoro vertex operator algebras $\mathcal{V}_c$. Our main result is construction of a minimal, strong set of generators of this subalgebra for any generic values of $c$. More precisely, we show that this vertex algebra is of type $(2,4,6^2,8^2,9,10^2,11,12^3)$. We also investigate two prominent examples of simple $S_3$-orbifold algebras corresponding to central charges $c=\frac12$ (Ising model) and $c=-\frac{22}{5}$ (i.e. $(2,5)$-minimal model). We prove that the former is a new unitary $W$-algebra of type $(2,4,6,8)$ and the latter is isomorphic to the affine simple $W$-algebra of type $\frak{g}_2$ at non-admissible level $-\frac{19}{6}$. We also provide another version of this isomorphism using the affine $W$-algebra of type $\frak{g}_2$ coming from a subregular nilpotent element.

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BibTeXRIS

Antun Milas, Michael Penn, Christopher Sadowski. 2022-09-27. $S_3$-Permutation Orbifolds of Virasoro Vertex Algebras. https://arxiv.org/abs/2209.13341

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