Characterization of 2D rational local conformal nets and its boundary conditions: the maximal case
Characterization of 2D rational local conformal nets and its boundary conditions: the maximal case
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DOI：
10.4171/dm/515
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发表时间：
2014-10
影响因子：
0.9
通讯作者：
M. Bischoff;Yasuyuki Kawahigashi;R. Longo
中科院分区：
文献类型：
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作者：
M. Bischoff;Yasuyuki Kawahigashi;R. Longo
设A是S1上的一个完全有理局部Mobius协变网，它描述了一组手征观测量。证明了二维Minkowski空间上包含手征理论A的局部Mobius协变网B2与酉模张量范畴DHR（A）中Q-系统的Morita等价类一一对应.这样的网B2的具有对称性A的Mobius协变边界条件由Morita等价类中的Q-系统或由对偶范畴的模自同构中的简单对象给出。我们推广到可约边界条件。为了建立这一结果，我们定义了Q-系统（特殊的对称β-Frobenius代数对象）和非退化辫子子因子的Morita等价的概念。本文证明了Kong和伦克尔的一个猜想，即广义Longo-Runren构造（α-归纳构造）与范畴满中心重合.这为辫状子因子的研究提供了新的视角和新的结果。
Let A be a completely rational local Mobius covariant net on S 1 , which describes a set of chiral observables. We show that local Mobius covari- ant nets B2 on 2D Minkowski space which contain the chiral theory A are in one-to-one correspondence with Morita equivalence classes of Q-systems in the unitary modular tensor category DHR(A). The Mobius covariant boundary con- ditions with symmetry A of such a net B2 are given by the Q-systems in the Morita equivalence class or by simple objects in the module category modulo automorphisms of the dual category. We generalize to reducible boundary con- ditions. To establish this result we define the notion of Morita equiva lence for Q- systems (special symmetric �-Frobenius algebra objects) and non-degenerately braided subfactors. We prove a conjecture by Kong and Runkel, namely that Rehren's construction (generalized Longo-Rehren constru ction,α-induction con- struction) coincides with the categorical full center. Thi s gives a new view and new results for the study of braided subfactors.