## Geometry & Topology

### Topological conformal field theories and gauge theories

Kevin Costello

#### 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.

#### Article information

Source
Geom. Topol., Volume 11, Number 3 (2007), 1539-1579.

Dates
Received: 9 June 2006
Accepted: 7 May 2007
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513799902

Digital Object Identifier
doi:10.2140/gt.2007.11.1539

Mathematical Reviews number (MathSciNet)
MR2326951

Zentralblatt MATH identifier
1139.32006

#### Citation

Costello, Kevin. Topological conformal field theories and gauge theories. Geom. Topol. 11 (2007), no. 3, 1539--1579. doi:10.2140/gt.2007.11.1539. https://projecteuclid.org/euclid.gt/1513799902

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