Fully Packed O(n=1) Model on Random Eulerian Triangulations

TL;DR

This paper introduces a matrix model for the fully-packed O(n) model on random Eulerian triangulations, revealing a shift in central charge and extending understanding of these models in quantum gravity contexts.

Contribution

It presents a new matrix model for the fully-packed O(n) model on Eulerian triangulations and explores the central charge shift for n=1 and general n cases.

Findings

For n=1, the model maps to a gravitational 6-vertex model with c=1.

The model exhibits a shift c -> c+1 when moving from ordinary to Eulerian triangulations.

The paper discusses the behavior for arbitrary n, extending the model's applicability.

Abstract

We introduce a matrix model describing the fully-packed O(n) model on random Eulerian triangulations (i.e. triangulations with all vertices of even valency). For n=1 the model is mapped onto a particular gravitational 6-vertex model with central charge c=1, hence displaying the expected shift c -> c+1 when going from ordinary random triangulations to Eulerian ones. The case of arbitrary n is also discussed.