Ocneanu Algebra of Seams: Critical Unitary $E_6$ RSOS Lattice Model

Paul A. Pearce, Jorgen Rasmussen
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Abstract

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.
奥克纳努接缝代数:临界单元 $E_6$ RSOS 晶格模型
我们把 $A$ 系列和特殊的 $E_6$ 限制固态-固态晶格模型视为临界杨-巴克斯特可积分二维 $A$-$D$-$E$ 晶格模型的原型。我们将重点放在 I 型理论上,该理论的特点是在连续缩放极限中存在扩展的手性对称性。从环面上列转移矩阵的换元族开始,我们建立了奥克纳努图融合代数的矩阵表示,作为任意有限大小晶格的可积分接缝,其结构常数由 Petkova 和 Zuber 规定。这个交换接缝代数包含韦林德、融合邻接和图融合代数。我们对奥克涅努代数的矩阵表示囊括了交换转移矩阵族的量子对称性。在连续缩放极限中,可积分接缝实现了相关共形场论的拓扑缺陷,而已知的环矩阵则编码了扭曲共形分割函数。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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