On the Continuum Limit of the Discrete Regge Model in 4d

TL;DR

This paper investigates the continuum limit of the 4d Discrete Regge model using Monte Carlo simulations, focusing on the potential second-order phase transition at negative gravity coupling to establish a connection to continuous spacetime.

Contribution

It provides a detailed analysis of the phase transition behavior in the 4d Discrete Regge model, exploring the conjectured second-order transition as a candidate for the continuum limit.

Findings

Identifies a potential second-order phase transition at negative gravity coupling.

Demonstrates that the finite link length restriction accelerates computations.

Provides critical discussion on the nature of the phase transition.

Abstract

The Regge Calculus approximates a continuous manifold by a simplicial lattice, keeping the connectivities of the underlying lattice fixed and taking the edge lengths as degrees of freedom. The Discrete Regge model employed in this work limits the choice of the link lengths to a finite number. This makes the computational evaluation of the path integral much faster. A main concern in lattice field theories is the existence of a continuum limit which requires the existence of a continuous phase transition. The recently conjectured second-order transition of the four-dimensional Regge skeleton at negative gravity coupling could be such a candidate. We examine this regime with Monte Carlo simulations and critically discuss its behavior.