论文标题
晶格顶点代数的Orbifolds
Orbifolds of Lattice Vertex Algebras
论文作者
论文摘要
对于一个正定定义的晶格$ Q $，可以将晶格顶点代数$ v_q $和任何自动形态$σ$ q $ q $ lifts与$ v_q $的自动形态相关联。在本文中，我们调查了Orbifold顶点algebra $ v_q^σ$，该元素由$ v_q $固定在$σ$下的$ v_q $的元素组成，如果$σ$具有Prime Order。我们明确描述了不可约的$ v_q^σ$ - 模块，计算其字符，并确定字符的模块化转换。作为一个应用程序，我们发现所有不可约$ v_q^σ$ - 模块的渐近和量子尺寸。我们详细考虑了$σ$的订单为$ 2 $或$ 3 $的情况，以及排列的Orbifolds。
To a positive-definite even lattice $Q$, one can associate the lattice vertex algebra $V_Q$, and any automorphism $σ$ of $Q$ lifts to an automorphism of $V_Q$. In this paper, we investigate the orbifold vertex algebra $V_Q^σ$, which consists of the elements of $V_Q$ fixed under $σ$, in the case when $σ$ has prime order. We describe explicitly the irreducible $V_Q^σ$-modules, compute their characters, and determine the modular transformations of characters. As an application, we find the asymptotic and quantum dimensions of all irreducible $V_Q^σ$-modules. We consider in detail the cases when the order of $σ$ is $2$ or $3$, as well as the case of permutation orbifolds.
