N=2极小共形域论与x^d的矩阵双分解
N=2 minimal conformal field theories and matrix bifactorisations of x^d
摘要：
证明了a）位势x^d-y^d的分次矩阵分解与b）中心荷为3-6/d的N=2极小超顶点算子代数的表示之间的满子范畴的张量等价性，其中d是奇数.子范畴由a）具有连续指标集的置换型矩阵分解和b）Neveu-Schwarz型表示给出。这一结果的物理动机是朗道-金兹伯格/共形域论对应，其中它相当于对应两侧缺陷子集的等价性。我们的工作建立在Brunner和Roggenkamp [arXiv：0707.0922]的结果基础上，其中建立了融合规则的同构。
英文摘要：
We prove a tensor equivalence between full subcategories of a) graded matrix factorisations of the potential x^d-y^d and b) representations of the N=2 minimal super vertex operator algebra at central charge 3-6/d, where d is odd. The subcategories are given by a) permutation-type matrix factorisations with consecutive index sets, and b) Neveu-Schwarz-type representations. The physical motivation for this result is the Landau-Ginzburg / conformal field theory correspondence, where it amounts to the equivalence of a subset of defects on both sides of the correspondence. Our work builds on results by Brunner and Roggenkamp [arXiv:0707.0922], where an isomorphism of fusion rules was established.
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