Asymptotic freedom and euclidean quantum gravity

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 4d 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 · 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.

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

“…The system of SU(2) gauge fields coupled to quantum gravity has the action [5] S = 2m 2 , with a 4-volume V t assigned to each triangle, describe the coupling of gravity to the gauge field. U t is the ordered product of SU(2) matrices around t. In contrast to the flat lattice, the unit matrix in the action is important because the weight factors are dynamical.…”

“…One remarkable finding was the discovery of an "entropy dominated", well-defined phase, where the expectation values with respect to the pure Regge-Einstein action are stable [2][3][4]. The next question addressed was the physical relevance of this regime which has been tested by coupling a non-Abelian gauge field to gravity [5]. If one assumes that the world without gravity is described by a grand unified asymptotically free theory, these numerical studies investigate the relation of the hadronic scale to the Planck scale.…”

Phase structure of SU(2) lattice gauge theory with quantum gravity

“…In ref. [6], see ref. [7] for a concise summary, a research program along this line of thought was outlined, and supported by exploratory numerical results from an 2 · 4 3 lattice.…”

“…[6] At m 2 P = 0.005 this system was investigated for various β values. This is a data point well inside the entropy-dominated region.…”

“…As in ref. [6] 20,000 thermalization sweeps were performed before measurement. The subsequent statistics for each histogram is β dependent and lies in the range 20,000-60,000 sweeps.…”