paper

The phase and critical point of quantum Einstein-Cartan gravity

arXiv:1112.1323 · doi:10.1016/j.physletb.2012.04.024

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.

15 pages, 7 figures, the version to appear in Phys. Lett. B. We have clarified that Eqs. (E.5) and (E.6) of Phys. Rev. D82 (2010) 064039 were obtained by using the strong coupling expansion in terms of (M^2_h/8g^2) = 0.1

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