论文标题
基于Takiff Superalgebras的共形场理论
On conformal field theories based on Takiff superalgebras
论文作者
论文摘要
我们基于Babichenko和Ridout引入的基于Tabiff代数和超级船长的构建形式，基于Tabiff代数和超级船长的结构。可以将takiff Superalgebras视为带有Z级的截断截断的超级甲壳虫，这是由于取下谎言superalgebra g并将其放置在s = 0，...，p-1的程度上而产生的。使用适当定义的非分类不变形式，我们表明，Takiff Superalgebras产生了具有中央电荷C = P SDIM（G）的共形场理论的家庭。由此产生的保形场理论是以标准方式定义的，即，根据WZW模型，它们将其借助Lagrangian描述，其手性能量动量张量是从通常的Sugawara构造中自然获得的。鉴于他们复杂的表示理论，他们提供了共形领域理论的有趣例子。
We revisit the construction of conformal field theories based on Takiff algebras and superalgebras that was introduced by Babichenko and Ridout. Takiff superalgebras can be thought of as truncated current superalgebras with Z-grading which arise from taking p copies of a Lie superalgebra g and placing them in the degrees s=0,...,p-1. Using suitably defined non-degenerate invariant forms we show that Takiff superalgebras give rise to families of conformal field theories with central charge c=p sdim(g). The resulting conformal field theories are defined in the standard way, i.e. they lend themselves to a Lagrangian description in terms of a WZW model and their chiral energy momentum tensor is the one obtained naturally from the usual Sugawara construction. In view of their intricate representation theory they provide interesting examples of conformal field theories.
