Multicritical Dynamical Triangulations and Topological Recursion

Abstract: We explore a continuum theory of multicritical dynamical triangulations and causal dynamical triangulations in two-dimensional quantum gravity from the perspective of the Chekhov-Eynard-Orantin topological recursion. The former model lacks a causal time direction and is governed by the two-reduced $W<sup>{(3)}$ algebra, whereas the latter model possesses a causal time direction and is governed by the full $W<sup>{(3)}$ algebra. We show that the topological recursion solves the Schwinger-Dyson equations for both models, and we explicitly compute several amplitudes.