Two-dimensional topological gravity, topological matter and intersection theory on moduli space

We propose a two-dimensional topological matter system associated to an arbitrary compact Lie group G. This topological quantum field theory is defined in terms of intersection theory on the space of based holomorphic maps from a Riemann surface to the based loop group ωG of G, and corresponds physically to the topological sigma model with ωG as the target space. This topological matter system may be naturally coupled to two-dimensional topological gravity and is also related to topological Yang-Mills theory in four dimensions. There appears also to be a connection between this theory and chiral models involving infinite-dimensional twistor space.