论文标题
Landau-Ginzburg/$ x^d $和模块张量类别的共形场理论对应
Landau-Ginzburg/Conformal Field Theory Correspondence for $x^d$ and Module Tensor Categories
论文作者
论文摘要
Landau-Ginzburg/保形场理论对应关系可以预测某些多项式矩阵分解类别和与$ n = 2 $ supersympersympermememmetric-Meterympricric Conformal Field理论相关的矩阵分解类别之间的张量当量。我们意识到任何$ d $的$ x^d $的信件，在先前的结果仅限于奇数$ d $的情况下。 我们的证明使用了一个事实，即通信的两面都携带模块张量类别的结构，而不是$ \ m athbb {z} _d $ graded的向量空间，配备了非脱位编织。这使我们能够描述一个对象生成的CFT侧，并使用它有效地提供函数实现张量等于等效的函子。
The Landau-Ginzburg/Conformal Field Theory correspondence predicts tensor equivalences between categories of matrix factorisations of certain polynomials and categories associated to the $N=2$ supersymmetric conformal field theories. We realise this correspondence for $x^d$ for any $d$, where previous results were limited to odd $d$. Our proof uses the fact that both sides of the correspondence carry the structure of module tensor categories over the category of $\mathbb{Z}_d$-graded vector spaces equipped with a non-degenerate braiding. This allows us to describe the CFT side as generated by a single object, and use this to efficiently provide a functor realising the tensor equivalence.
