Multicritical Dynamical Triangulations and Topological Recursion

TL;DR

This paper applies topological recursion to analyze two-dimensional quantum gravity models, multicritical and causal dynamical triangulations, revealing their algebraic structures and solving their Schwinger-Dyson equations.

Contribution

It demonstrates that topological recursion can solve the Schwinger-Dyson equations for these models and clarifies their algebraic differences.

Findings

Topological recursion solves Schwinger-Dyson equations for both models.

Explicit computations of several amplitudes are provided.

The models are distinguished by their algebraic structures and causal properties.

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 $W^{(3)}$ 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.