The conformal geometry of Random Regge Triangulations

TL;DR

This paper explores the conformal geometry of random Regge triangulations in 2D quantum gravity, focusing on the regularized Liouville action and its mathematical connections.

Contribution

It introduces a detailed analysis of the conformal structure and Liouville action for random Regge triangulations, linking quantum gravity models with advanced geometric theories.

Findings

Established the connection between Liouville action and Regge triangulations.

Linked conformal geometry with Hodge-Deligne theory.

Provided insights into the geometric structure of 2D quantum gravity models.

Abstract

We review some of our recent work on the conformal geometry corresponding to the triangulated surfaces used in 2-dimensional simplicial quantum gravity. In particular, we discuss the regularized Liouville action associated with random Regge triangulations and its connection with Hodge-Deligne theory.