Models of discretized moduli spaces, cohomological field theories, and Gaussian means

Abstract

We prove combinatorially the explicit relation between genus filtrated s-loop means of the Gaussian matrix model and terms of the genus expansion of the Kontsevich-Penner matrix model (KPMM). The latter is the generating function for volumes of discretized (open) moduli spaces Mg,sdisc given by Ng,s(P1,... Ps) for (P1,. .,Ps)∈Z+s. This generating function therefore enjoys the topological recursion, and we prove that it is simultaneously the generating function for ancestor invariants of a cohomological field theory thus enjoying the Givental decomposition. We use another Givental-type decomposition obtained for this model by the second authors in 1995 in terms of special times related to the..