洛伦兹格点共形场论的有理性及相关模张量范畴
Rationality of Lorentzian Lattice CFTs And The Associated Modular Tensor Category
AI总结：
该研究对有理洛伦兹格点顶点算子代数的不可约模、缠结算子及融合规则进行分类，构建相关模张量范畴的模数据与辫子、融合矩阵，并验证特定格点对应的共形场论可实现指定Kac-Moody模张量范畴。
摘要：
我们基于符号为$(m,n)$的偶自对偶洛伦兹格点$\Lambda\subset\mathbb{R}^{m,n}$，对有理洛伦兹格点顶点算子代数（LLVOA）的不可约模进行了分类。我们证明，LLVOA的不可约模同构类集合，与某一子集$\Lambda_0^\circ\subset\mathbb{R}^{m,n}$及满秩子格$\Lambda_0\subset\Lambda$对应的等价类$\Lambda_0^\circ/\Lambda_0$一一对应。我们还对模之间的缠结算子进行了分类，并计算了融合规则。随后我们描述了与有理洛伦兹格点共形场论（LLCFT）相关的模张量范畴（MTC）的标准构造，明确构建了该MTC的模数据以及辫子矩阵和融合矩阵。作为具体示例，我们证明基于$m$为偶数的符号$(m,n)$偶自对偶洛伦兹格点的LLCFT，可实现$D(m \bmod 8)$ level 1 Kac-Moody MTC。
英文摘要：
We classify the irreducible modules of a rational Lorentzian lattice vertex operator algebra (LLVOA) based on an even, self-dual Lorentzian lattice $Λ\subset\mathbb{R}^{m,n}$ of signature $(m,n)$. We show that the set of isomorphism classes of irreducible modules of the LLVOA are in one-to-one correspondence with the equivalence classes $Λ_0^\circ/Λ_0$ for a certain subset $Λ_0^\circ\subset\mathbb{R}^{m,n}$ and a full rank sublattice $Λ_0\subsetΛ$. We also classify the intertwining operators between the modules and calculate the fusion rules. We then describe the standard construction of modular tensor category (MTC) associated to rational LLCFTs. We explicitly construct the modular data and braiding and fusing matrices for the MTC. As a concrete example, we show that the LLCFT based on a certain even, self-dual Lorentzian lattice of signature $(m, n)$, with $m$ even, realizes the $D(m \bmod 8)$ level 1 Kac-Moody MTC.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
