Gauge theories and two-dimensional field theories

These two papers concern the relationship between string-theory type objects and gauge theories.  

Topological conformal field theories and gauge theories. math.QA/0605647 Geometry & Topology, 11 (2007) 1539-1579.

This paper shows how to construct, from certain gauge-theory type data, a collection of differential forms on the moduli spaces of Riemann surfaces (using heat kernels). Formally, the integral of these differential forms is the partition function of associated gauge theory.  However, these integrals don't converge, because the forms have singularities at the boundary of the moduli space of surfaces.   These singlurities correspond to the singularities in Feynman graphs.

An example of this procedure arises from the Yang-Mills gauge theory.  As a corollary, we see that, for any 4 manifold, one can construct a 3 dimensional Calabi-Yau category whose objects are Yang-Mills bundles.  

Closed String TCFT for Hermitian Calabi-Yau Elliptic Spaces. Joint with Thomas Tradler and Mahmoud Zeinalian.  arXiv:0807.3052 

The previous paper showed how to construct an open-string field theory from the gauge theory data. This paper gives an explicit construction of the associated closed-string theory.