Abstract
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.
Citation
Kevin Costello. "Topological conformal field theories and gauge theories." Geom. Topol. 11 (3) 1539 - 1579, 2007. https://doi.org/10.2140/gt.2007.11.1539
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