1112.1323 (She-Sheng Xue)

The phase and critical point of quantum Einstein-Cartan gravity    [PDF]

She-Sheng Xue

By introducing diffeomorphism and local Lorentz gauge invariant holonomy
fields, we study in the recent article [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 article 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.

View original: http://arxiv.org/abs/1112.1323