Galois共轭张量融合范畴与非酉CFT
Galois conjugated tensor fusion categories and non-unitary CFT
摘要：
我们提供了一个概括的矩阵乘积算子（MPO）的形式主义弦网投影纠缠对态（PEPS），包括非酉解的五边形方程。这些状态提供了明确的晶格实现的伽罗瓦共轭对应的（2+1）维TQFT，基于张量融合类别。虽然这些重整化群不动点态的父哈密顿是非厄米的，但由于五边形方程，这些态的许多拓扑性质仍然成立。我们通过例子表明，杨-李理论（斐波那契融合范畴的非酉对应物）的拓扑部门可以构建，即使在没有封闭下的厄密共轭的Ocneanu管代数的基本元素。我们认为，这可以推广到所有$SU(2)$级别的$k$模型的非酉解。拓扑部门的建设表明，通过应用奇怪的概念，杨-李模型，产生了一个非酉版本的经典硬六边形模型在杨-李普适类，并获得所有广义扭曲边界条件的有限柱的杨-李边缘奇异性。
英文摘要：
We provide a generalisation of the matrix product operator (MPO) formalism for string-net projected entangled pair states (PEPS) to include non-unitary solutions of the pentagon equation. These states provide the explicit lattice realisation of the Galois conjugated counterparts of (2+1) dimensional TQFTs, based on tensor fusion categories. Although the parent Hamiltonians of these renormalisation group fixed point states are non-Hermitian, many of the topological properties of the states still hold, as a result of the pentagon equation. We show by example that the the topological sectors of the Yang-Lee theory (the non-unitary counterpart of the Fibonacci fusion category) can be constructed even in the absence of closure under Hermitian conjugation of the basis elements of the Ocneanu tube algebra. We argue that this can be generalised to the non-unitary solutions of all $SU(2)$ level $k$ models. The topological sector construction is demonstrated by applying the concept of strange correlators to the Yang-Lee model, giving rise to a non-unitary version of the classical hard hexagon model in the Yang-Lee universality class and obtaining all generalised twisted boundary conditions on a finite cylinder of the Yang-Lee edge singularity.
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