# Phase diagram of Regge quantum gravity coupled to SU(2) gauge theory

## TL;DR

This paper investigates the phase structure of Regge quantum gravity coupled with SU(2) gauge theory on various lattices, revealing stable geometrical phases and potential for a physical continuum limit.

## Contribution

It provides the first detailed analysis of the phase diagram of coupled Regge quantum gravity and SU(2) gauge theory on multiple lattice sizes.

## Key findings

- Stable geometrical expectation values extend to negative couplings.
- The string tension scales consistently with the gauge theory beta-function.
- A possible physical limit through scaling is identified.

## Abstract

We analyze Regge quantum gravity coupled to SU(2) gauge theory on $4^3\times 2$, $6^{3}\times 4$ and $8^{3}\times 4$ simplicial lattices. It turns out that the window of the well-defined phase of the gravity sector where geometrical expectation values are stable extends to negative gravitational couplings as well as to gauge couplings across the deconfinement phase transition. We study the string tension from Polyakov loops, compare with the $\beta$-function of pure gauge theory and conclude that a physical limit through scaling is possible.