Integrable and conformal twisted boundary conditions for sl(2) A-D-E lattice models
Integrable and conformal twisted boundary conditions for sl(2) A-D-E lattice models
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sl(2) A-D-E 晶格模型的可积和共形扭曲边界条件
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发表时间：
2002
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通讯作者：
P. Pearce
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作者：
C. Chui;C. Mercat;P. Pearce
本文研究了环面上s2幺正极小模型的共形扭曲边界条件的可积实现。这些共形场论被实现为具有正谱参数u> 0和Coxete数g的临界G = A，D，E格点模型的连续标度极限。通常的A-型融合被标记为Kac标签（r，s）并且与Ve rlinde融合代数相关联。在图融合代数的两个辫子极限u →± i∞中引入了一种新的融合，分别用a，B ∈ G标记.当与自同构结合时，它们会导致一般的可积缝，标记为x =（r，a，B，κ）∈（Ag−2，H，H，Z2），其中H是I型理论的图G和II型理论的父图。将我们的构造标号与Petkova和Zuber的共形标号相一致，我们发现可积缝与共形缝是一一对应的.因此，不同的接缝与Ocneanu量子图的节点相关联。量子对称性和扭曲的配分函数进行了数值检查，|G|六、我们还表明，在D2的情况下，t帽子的Ocneanu代数的接缝的非交换性出现，因为自同构不与融合交换。
We study integrable realizations of conformal twisted boundary conditions for s�( 2) unitary minimal models on a torus. These conformal field theories are realized as the continuum scaling limit of critical G = A, D, E lattice models with positive spectral parameter u> 0a nd Coxete rnumber g .I ntegrable seams are constructed by fusing blocks of elementary local face weights. The usual A-type fusions are labelled by the Kac labels (r, s) and are associated with the Ve rlinde fusion algebra. We introduce a new type of fusion in the two braid limits u →± i∞ associated with the graph fusion algebra, and labelled by nodes a, b ∈ G respectively. When combined with automorphisms, they lead to general integrable seams labelled by x = (r, a ,b , κ)∈ (Ag−2 ,H , H,Z2) where H is the graph G for type I theories and its parent for type II theories. Identifying our construction labels with the conformal labels of Petkova and Zuber, we find that the integrable seams are in one-to-one correspondence with th ec onformal seams. The distinct seams are thus associated with the nodes of the Ocneanu quantum graph. The quantum symmetries and twisted partition functions are checked numerically for |G| 6. We also show, in the case of D2� ,t hat the non-commutativity of the Ocneanu algebra of seams arises because the automorphisms do not commute with the fusions.