论文标题
费米子CFT和代数分类
Fermionic CFTs and classifying algebras
论文作者
论文摘要
我们在存在边界，缺陷和界面的情况下研究具有自旋结构的表面上的费米子共形场理论。我们获得了相关的交叉关系，特别注意奇偶校验符号和符号，这是由于自旋结构在不同限制下的变化而产生的。我们为边界，缺陷和接口定义了费米子分类的代数，这使人们可以读取基本边界条件等。 作为示例，我们定义了Virasoro最小模型的费米子扩展，并为频谱和批量结构常数提供明确的解决方案。我们展示了$ a $ - 和$ d $ type的费米米奇virasoro最小型号与我们通常定义的奇偶校正操作相关。我们研究了几个示例中的界限，缺陷和界面，特别是在费尔米金的模型中，即在费米子三临界模型中的自由费用，即第一个单位$ n = 1 $ n = 1 $超构建最小模型，以及与超级符号的Lee-yang模型相关的，这是两个不同的范围。
We study fermionic conformal field theories on surfaces with spin structure in the presence of boundaries, defects, and interfaces. We obtain the relevant crossing relations, taking particular care with parity signs and signs arising from the change of spin structure in different limits. We define fermionic classifying algebras for boundaries, defects, and interfaces, which allow one to read off the elementary boundary conditions, etc. As examples, we define fermionic extensions of Virasoro minimal models and give explicit solutions for the spectrum and bulk structure constants. We show how the $A$- and $D$-type fermionic Virasoro minimal models are related by a parity-shift operation which we define in general. We study the boundaries, defects, and interfaces in several examples, in particular in the fermionic Ising model, i.e. the free fermion, in the fermionic tri-critical Ising model, i.e. the first unitary $N=1$ superconformal minimal model, and in the supersymmetric Lee-Yang model, of which there are two distinct versions that are related by parity-shift.
