Phase Structure of Four-dimensional Simplicial Quantum Gravity with a U(1) Gauge Field

TL;DR

This study investigates the phase structure of four-dimensional simplicial quantum gravity coupled with U(1) gauge fields, revealing a new smooth phase and analyzing the nature of phase transitions through Monte Carlo simulations.

Contribution

It introduces the existence of a smooth phase in the model with gauge fields and suggests a higher order phase transition, enabling potential continuum limit studies.

Findings

Discovery of a smooth phase between crumpled and branched polymer phases.

Identification of a higher order phase transition at the critical point.

Numerical evidence supporting the possibility of a continuum limit.

Abstract

The phase structure of four-dimensional simplicial quantum gravity coupled to U(1) gauge fields has been studied using Monte-Carlo simulations. The smooth phase is found in the intermediate region between the crumpled phase and the branched polymer phase. This new phase has a negative string susceptibility exponent, even if the number of vector fields (Nv) is 1. The phase transition between the crumpled phase and the smooth phase has been studied by a finite size scaling method. From the numerical results, we expect that this model (coupled to one gauge field) has a higher order phase transition than first order, which means the possibility to take the continuum limit at the critical point. Furthermore, we consider a modification of the balls-in-boxes model for a clear understanding of the relation between the numerical results and the analytical one.