Asymptotic Freedom and Euclidean Quantum Gravity

TL;DR

This paper explores Euclidean quantum gravity effects using lattice gauge theory simulations, revealing stable bulk expectation values and a remnant of the QCD phase transition in a strong gravity regime.

Contribution

It introduces a numerical simulation of 4D SU(2) lattice gauge theory coupled with Regge calculus to study quantum gravity effects.

Findings

Stable bulk expectation values vary smoothly with gauge coupling.

Remnant of QCD deconfining phase transition observed.

Exploratory results in strong gravity regime with comparable Planck and hadronic masses.

Abstract

Pure SU(2) gauge theory is the simplest asymptotically free theory in four dimensions. To investigate Euclidean quantum gravity effects in a fundamental length scenario, we simulate 4$d$ SU(2) lattice gauge theory on a dynamically coupled Regge skeleton. The fluctuations of the skeleton are governed by the standard Regge-Einstein action. From a small $2\cdot 4^3$ lattice we report exploratory numerical results, limited to a region of strong gravity where the Planck mass and hadronic masses take similar orders of magnitude. We find a range of the Planck mass where stable bulk expectation values are obtained which vary smoothly with the gauge coupling, and a remnant of the QCD deconfining phase transition is located. Note: The full ps file of this preprint is also available via anonymous ftp to ftp.scri.fsu.edu. To get the ps file, ftp to this address and use for username "anonymous" and for password your name. The file is in the directory pub/krishnan (to go to that directory type: cd pub/krishnan) and is called gravity.ps (to get it type: get gravity.ps). If you have any problems send mail to krishnan@ds1.scri.fsu.edu.