CDT coupled to dimer matter: An analytical approach via tree bijections

TL;DR

This paper presents an analytical solution for a hard dimers model coupled to 2D causal dynamical triangulations using combinatorial bijections, revealing insights into the model's scaling limit and multi-critical behavior.

Contribution

It introduces a novel combinatorial bijection approach to solve the coupled dimers and CDT model and connects it to multi-critical points in transfer matrix analysis.

Findings

Analytical solution via bijections for the coupled model

Identification of the scaling limit from a multi-critical point

Connection between combinatorial and matrix model approaches

Abstract

We review a recently obtained analytical solution of a restricted so-called hard dimers model coupled to two-dimensional CDT. The combinatorial solution is obtained via bijections of causal triangulations with dimers and decorated trees. We show that the scaling limit of this model can also be obtained from a multi-critical point of the transfer matrix for dynamical triangulations of triangles and squares when one disallows for spatial topology changes to occur.