2-dimensional Regge gravity in the conformal gauge

TL;DR

This paper develops a discretized path integral formulation of 2D quantum gravity using Regge geometries in the conformal gauge, providing exact expressions for key determinants and analyzing diffeomorphism roles.

Contribution

It introduces a Regge-based discretization of 2D quantum gravity path integral in the conformal gauge with exact Faddeev-Popov determinant expressions.

Findings

Derived exact Faddeev-Popov determinant for Regge surfaces

Showed the discretized model converges to the continuum result

Analyzed the impact of diffeomorphisms in the Regge framework

Abstract

By restricting the functional integration to the Regge geometries, we give the discretized version of the well known path integral formulation of 2--dimensional quantum gravity in the conformal gauge. We analyze the role played by diffeomorphisms in the Regge framework and we give an exact expression for the Faddeev--Popov determinant related to a Regge surface; such an expression in the smooth limit goes over to the correct continuum result.