论文标题
顶点操作员超级甲虫和16倍方式
Vertex operator superalgebras and 16-fold way
论文作者
论文摘要
让$ v $是带有自然订单2自然形态$σ$的顶点操作员超级级。在$ v $的适当条件下，$σ$ -fixed子空间$ v _ {\ bar 0} $是顶点操作员代数和类别$ c_ {v _ {\ bar 0}} $ of $ v _ {\ bar 0} $ - modules- modules是模块化的Tensor tensor tensor类别。在本文中，我们证明了$ c_ {v _ {\ bar 0}} $是一个费米子模块化张量类别，mügerCentralizer$ c_ { 0} $ - $ V $ - 模块的子模块。特别是，$ c_ {v _ {\ bar 0}}^0 $是超模型张量类别，$ c_ {v _ {\ bar 0}} $是$ c_ {v _ {\ bar 0}}}}^0 $的最小模块扩展。我们为每个正整数$ l $ $ v^l $提供了一个$ c_ {v^l _ {\ bar 0}} $的构造是$ c_ {v _ {v _ {\ bar 0}}}^0 $的最小模块化扩展。我们证明这些模块化张量类别$ c_ {v^l _ {\ bar 0}} $由$ l $ modulo 16的一致性类别独特地确定，直到等效。
Let $V$ be a vertex operator superalgebra with the natural order 2 automorphism $σ$. Under suitable conditions on $V$, the $σ$-fixed subspace $V_{\bar 0}$ is a vertex operator algebra and the category $C_{V_{\bar 0}}$ of $V_{\bar 0}$-modules is modular tensor category. In this paper, we prove that $C_{V_{\bar 0}}$ is a fermionic modular tensor category and the Müger centralizer $C_{V_{\bar 0}}^0$ of the fermion in $C_{V_{\bar 0}}$ is generated by the irreducible $V_{\bar 0}$-submodules of the $V$-modules. In particular, $C_{V_{\bar 0}}^0$ is a super-modular tensor category and $C_{V_{\bar 0}}$ is a minimal modular extension of $C_{V_{\bar 0}}^0$. We provide a construction of a vertex operator $V^l$ for each positive integer $l$ such that $C_{V^l_{\bar 0}}$ is minimal modular extension of $C_{V_{\bar 0}}^0$. We prove that these modular tensor categories $C_{V^l_{\bar 0}}$ are uniquely determined, up to equivalence, by the congruence class of $l$ modulo 16.
