A Laplacian to Compute Intersection Numbers on (M)g ,n and Correlation Functions in NCQFT

Let F-g(t) be the generating function of intersection numbers of psi-classes on the moduli spaces (M)(g ,n )of stable complex curves of genus-g. As by-product of a complete solution of all non-planar correlation functions of the renormalised Phi(3)-matrical QFT model, we explicitly construct a Laplacian delta t on a space of formal parameters t(i) which satisfies exp( n-expressionry sumexpressiontion g >= 2N2-2gFg(t))=exp((-delta t+F-2(t))/N-2)1 as formal power series in 1/N-2. The result is achieved via Dyson-Schwinger equations from noncom-mutative quantum field theory combined with residue techniques from topological recursion. The genus-g correlation functions of the Phi(3)-matricial QFT model are obtained by repeated application of another differential operator to F-g(t)and taking for t(i) the renormalised moments of a measure constructed from the covariance of the model.

Automated summary

This paper explicitly constructs the generating function F-g(t) of intersection numbers of psi-classes on the moduli spaces (M)(g ,n) of stable complex curves of genus-g, by using Dyson-Schwinger equations from noncom-mutative quantum field theory combined with residue techniques from topological recursion. The genus-g correlation functions of the Phi(3)-matricial QFT model are obtained by repeated application of another differential operator to F-g(t) and taking for t(i) the renormalised moments of a measure constructed from the covariance of the model.