The phase and critical point of quantum Einstein-Cartan gravity

TL;DR

This paper investigates the phase structure of quantum Einstein-Cartan gravity using holonomy fields, identifying an order-disorder phase transition and estimating the critical point where continuum theory may emerge.

Contribution

It introduces a gauge-invariant holonomy field framework to analyze phase transitions in quantum Einstein-Cartan gravity within Regge calculus.

Findings

Identifies long-range and short-range phases of holonomy fields.

Estimates the ultra-violet critical point for phase transition.

Discusses conditions for continuum limit of quantum gravity.

Abstract

By introducing diffeomorphism and local Lorentz gauge invariant holonomy fields, we study in the recent article [S.-S. Xue, Phys. Rev. D82 (2010) 064039] the quantum Einstein-Cartan gravity in the framework of Regge calculus. On the basis of strong coupling expansion, mean-field approximation and dynamical equations satisfied by holonomy fields, we present in this Letter calculations and discussions to show the phase structure of the quantum Einstein-Cartan gravity, (i) the order phase: long-range condensations of holonomy fields in strong gauge couplings; (ii) the disorder phase: short-range fluctuations of holonomy fields in weak gauge couplings. According to the competition of the activation energy of holonomy fields and their entropy, we give a simple estimate of the possible ultra-violet critical point and correlation length for the second-order phase transition from the order phase to disorder one. At this critical point, we discuss whether the continuum field theory of quantum Einstein-Cartan gravity can be possibly approached when the macroscopic correlation length of holonomy field condensations is much larger than the Planck length.