Geometry of 4d Simplicial Quantum Gravity with a U(1) Gauge Field

TL;DR

This paper investigates the geometric properties of four-dimensional simplicial quantum gravity coupled with a U(1) gauge field through numerical simulations, revealing a continuous phase transition and an inflated, symmetric geometry at criticality.

Contribution

It provides the first numerical analysis of 4D simplicial quantum gravity with a U(1) gauge field, identifying phase transition characteristics and geometric features at critical points.

Findings

Continuous phase transition observed with gauge coupling.

Inflated, homogeneous, and symmetric geometry at criticality.

Measured scalar curvature and geometric properties of S^4 space.

Abstract

The geometry of 4D simplicial quantum gravity with a U(1) gauge field is studied numerically. The phase diagram shows a continuous transition when gravity is coupled with a U(1) gauge field. At the critical point measurements of the curvature distribution of S^4 space shows an inflated geometry with homogeneous and symmetric nature. Also, by choosing a 4-simplex and fixing the scalar curvature geometry of the space is measured.