R. Dijkgraaf, E. Witten, "Mean field theory, topological field theory, and multi-matrix models," Nuclear Physics B, 342:486-522, 1990.
Robert Dijkgraaf (Joseph Henry Laboratories, Princeton University):
"The correct quantum mechanical treatment of gravity is still one of the great enigmas in theoretical physics. It would constitute the unification of the two great principles of modern physics: general relativity and quantum mechanics. Recently, these problems have been solved in the `toy model' of two instead of four dimensions by means of triangulation techniques.
"Our paper constitutes an alternative approach to the issue of quantum gravity along the lines of topological gravity, which can be considered as a simpler, more tractable phase of two-dimensional gravity. This field theory is completely solvable, and its solution can be used to analyze the nontrivial phase, as well.
"We show that even for more complicated systems, consisting of matter fields and gravity, this equivalence with topological models ...
