t Hooft expansion of multi-boundary correlators in 2D topological gravity

We study multi-boundary correlators of Witten-Kontsevich topological gravity in two dimensions. We present a method of computing an open string like expansion, which we call the t Hooft expansion, of the $n$-boundary correlator for any $n$ up to any order by directly solving the Korteweg-De Vries equation. We first explain how to compute the t Hooft expansion of the one-boundary correlator. The algorithm is very similar to that for the genus expansion of the open free energy. We next show that the t Hooft expansion of correlators with more than one boundary can be computed algebraically from the correlators with a lower number of boundaries. We explicitly compute the t Hooft expansion of the $n$-boundary correlators for $n=1,2,3$. Our results reproduce previously obtained results for Jackiw-Teitelboim gravity and also the t Hooft expansion of the exact result of the three-boundary correlator which we calculate independently in the Airy case.