Topological and conformal field theory as Frobenius algebras
Topological and conformal field theory as Frobenius algebras
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DOI：
10.1090/conm/431/08275
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发表时间：
2005-12
期刊：
影响因子：
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通讯作者：
I. Runkel;Jens Fjelstad;J. Fuchs;C. Schweigert
中科院分区：
文献类型：
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作者：
I. Runkel;Jens Fjelstad;J. Fuchs;C. Schweigert
二维共形场论（CFT）可以通过它的相关函数来定义。它们必须满足某些一致性条件，这些条件是由世界片沿沿着圆或间隔切割而产生的。一个（有理）CFT的构造可以分为两个步骤，其中一个是复解析的，另一个是纯代数的。我们实现的代数部分的建设与三维拓扑场论的帮助下，并表明，任何对称的特殊Frobenius代数在适当的编织monoidal类别产生的解决方案。二维拓扑场论提供了一类特殊的例子，其中相关的么半群范畴是向量空间范畴。
Two-dimensional conformal field theory (CFT) can be defined through its correlation functions. These must satisfy certain consistency conditions which arise from the cutting of world sheets along circles or intervals. The construction of a (rational) CFT can be divided into two steps, of which one is complex-analytic and one purely algebraic. We realise the algebraic part of the construction with the help of three-dimensional topological field theory and show that any symmetric special Frobenius algebra in the appropriate braided monoidal category gives rise to a solution. A special class of examples is provided by two-dimensional topological field theories, for which the relevant monoidal category is the category of vector spaces.