Topological conformal field theories and gauge theories
Topological conformal field theories and gauge theories
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拓扑共形场论和规范场论
DOI：
10.2140/gt.2007.11.1539
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发表时间：
2006
影响因子：
2
通讯作者：
K. Costello
中科院分区：
文献类型：
--
作者：
K. Costello
本文给出了使用热核在度量带状图的模空间上或等效地在有边界的黎曼曲面的模空间上的微分形式的构造。该构造取决于具有弗罗贝尼乌斯代数丛的流形，满足各种条件。这些形式满足粘合条件，这意味着它们形成了开放拓扑共形场论，即一种开弦理论。如果这些形式的积分收敛，就会产生陈-西蒙斯型规范理论的配分函数的纯量子部分。四流形的杨-米尔斯理论是作为陈-西蒙斯型规范理论之一而出现的。
This paper gives a construction, using heat kernels, of differential forms on the moduli space of metrised ribbon graphs, or equivalently on the moduli space of Riemann surfaces with boundary. The construction depends on a manifold with a bundle of Frobenius algebras, satisfying various conditions. These forms satisfy gluing conditions which mean they form an open topological conformal field theory, that is, a kind of open string theory. If the integral of these forms converged, it would yield the purely quantum part of the partition function of a Chern-Simons type gauge theory. Yang-Mills theory on a four manifold arises as one of these Chern-Simons type gauge theories.