洛伦兹晶格 CFT 的合理性及相关的模态张量类别

arXiv - MATH - Quantum Algebra Pub Date : 2024-08-05 DOI:arxiv-2408.02744

Ranveer Kumar Singh, Madhav Sinha, Runkai Tao

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引用次数: 0

摘要

我们讨论了最近在 arXiv:2312.16296 中构建的洛伦兹晶格共形场论（LLCFT）的合理性，并得到了等效的合理性描述，概括了温德兰的合理纳兰 CFT 描述。然后，我们描述了与有理 LLCFT 相关的模块张量类别（MTC）的构造。我们为 MTC 明确地构造了模块数据以及编织矩阵和融合矩阵。作为一个具体例子，我们展示了基于某个偶数、自偶洛伦兹晶格的LLCFT，其签名为$(m,n)$，其中$m$为偶数，实现了$D(m\bmod 8)$级1Kac-Moody MTC。

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Rationality of Lorentzian Lattice CFTs And The Associated Modular Tensor Category

We discuss the rationality of Lorentzian lattice conformal field theory (LLCFT) recently constructed in arXiv:2312.16296 and obtain equivalent characterizations of rationality generalising Wendland's rational Narain CFT characterization. We then describe the construction of a 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 realises the $D(m\bmod 8)$ level 1 Kac-Moody MTC.

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arXiv - MATH - Quantum Algebra

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