论文标题
$ s_3 $ - virasoro顶点代数的permunt orbifolds
$S_3$-Permutation Orbifolds of Virasoro Vertex Algebras
论文作者
论文摘要
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 $。我们的主要结果是为任何$ c $的通用值建造了该子代理的最小，强大的发电机。更确切地说，我们表明该顶点代数为$（2,4,6^2,8^2,9,10^2,11,12^3）$。 我们还研究了两个简单的$ S_3 $ -ORBIFOLD代数的突出示例，这些代数对应于中央费用$ C = \ frac12 $（ISING型号）和$ C = - \ frac {22} {5} $（即$（I.E. $（$（2,5）$ - 最小模型）。我们证明，前者是$ $（2,4,6,8）$的新型unital $ w $ -algebra，后者对affine simple $ w $ -w $ -algebra的同构是$ \ frak {g} _2 $ of-Admissible Level $ - \ frac $ - \ frac $ - \ frac $ - \ frac {19} {6} $。我们还使用类型$ \ frak {g} _2 $来自nilpotent元素的offine $ w $ -algebra提供了此同构的另一个版本。
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.
