接缝的 Ocneanu 代数：临界幺正 $E_6$ RSOS 格点模型
Ocneanu Algebra of Seams: Critical Unitary $E_6$ RSOS Lattice Model
AI总结：
本文以临界幺正 $E_6$ RSOS 模型为对象，构建 Ocneanu 图融合代数的有限格点矩阵表示，证明可积接缝在标度极限下实现共形场论拓扑缺陷。
摘要：
我们将 $A$ 系列和例外的 $E_6$ Restricted Solid-On-Solid（受限固-固，RSOS）格点模型视为临界 Yang-Baxter 可积二维 $A$-$D$-$E$ 格点模型的典型例子。我们关注 I 型理论，其特征是在连续统标度极限中存在扩展手征对称性。从环面上列转移矩阵的对易族出发，我们将 Ocneanu 图融合代数的矩阵表示构建为任意有限尺寸格点的可积接缝，其结构常数由 Petkova 和 Zuber 给出。这种交换接缝代数包含 Verlinde、融合邻接和图融合代数作为子代数。我们对 Ocneanu 代数的矩阵表示概括了转移矩阵对易族的量子对称性。在连续统标度极限中，可积接缝实现了相关共形场论的拓扑缺陷，而已知的环面矩阵则编码了扭曲共形配分函数。
英文摘要：
We consider the $A$ series and exceptional $E_6$ Restricted Solid-On-Solid lattice models as prototypical examples of the critical Yang-Baxter integrable two-dimensional $A$-$D$-$E$ lattice models. We focus on type I theories which are characterized by the existence of an extended chiral symmetry in the continuum scaling limit. Starting with the commuting family of column transfer matrices on the torus, we build matrix representations of the Ocneanu graph fusion algebra as integrable seams for arbitrary finite-size lattices with the structure constants specified by Petkova and Zuber. This commutative seam algebra contains the Verlinde, fused adjacency and graph fusion algebras as subalgebras. Our matrix representation of the Ocneanu algebra encapsulates the quantum symmetry of the commuting family of transfer matrices. In the continuum scaling limit, the integrable seams realize the topological defects of the associated conformal field theory and the known toric matrices encode the twisted conformal partition functions.
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