Multicritical Dynamical Triangulations and Topological Recursion

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 $W^{(3)}$ algebra, whereas the latter model possesses a causal time direction and is governed by the full $W^{(3)}$ algebra. We show that the topological recursion solves the Schwinger-Dyson equations for both models, and we explicitly compute several amplitudes.

💡 Research Summary

This paper investigates two‑dimensional quantum gravity through the lens of multicritical dynamical triangulations (DT) and causal dynamical triangulations (CDT), and demonstrates that both families of models are solved exactly by the Chekhov‑Eynard‑Orantin (CEO) topological recursion. The authors begin by reviewing the standard matrix‑model description of pure DT, which corresponds to Liouville gravity with central charge c = 0. In the continuum limit the generating functional is expressed in terms of creation and annihilation operators (\phi^\dagger_\ell,\phi_\ell) and a Hamiltonian that respects a “no big‑bang” condition, i.e. the vacuum is annihilated by the Hamiltonian. By introducing a star‑map that translates operator expressions into differential operators acting on source variables (j_\ell), they rewrite the Hamiltonian in terms of the two‑reduced (W^{(3)}) algebra: \