Conformally invariant gauge fixed actions for 2-D topological gravity
It seems that topology has benefited more from the marriage between the precise science of topology and the phenomenological science of quantum field theory. As is a now familiar story, S. K. Donaldson discovered new invariants for four-manifolds with the help of the new science of topological quantum field theory. In the present work, the authors show that the Mumford invariants for moduli spaces of curves [\textit{D. Mumford}, Arithmetic and geometry, Pap. dedic. I. R. Shafarevich, Vol. II: Geometry, Prog. Math. 36, 271-328 (1983; Zbl 0554.14008)] can be obtained from a gauge fixed action of a topological quantum field theory in two dimensions. The method bears remarkable similarity to that of S. K. Donaldson in discovering his famous invariants [for a recent description of the Donaldson invariants see \textit{S. K. Donaldson} and \textit{P. B. Kronheimer}, The geometry of four manifolds (Clarendon Press, Oxford) (1990)].
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