The phase and critical point of quantum Einstein-Cartan gravity

She-Sheng Xue

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The phase and critical point of quantum Einstein-Cartan gravity

She-Sheng Xue

High Energy Physics - Theory · Submitted 3 Dec 2011

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim 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.

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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.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	By introducing diffeomorphism and local Lorentz gauge invariant holonomy fields, we study in the recent article [S.-S.	contribution 0.49	0.61	0.02	unclear 0.55
s1	Xue, Phys. Rev. D82 (2010) 064039] the quantum Einstein-Cartan gravity in the framework of Regge calculus.	background 0.73	0.20	0.03	asserted 0.91
s2	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.	result 0.74	0.93	0.59	asserted 1.00
s3	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.	result 0.74	0.93	0.25	hedged possibility 0.76
s4	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.	interpretation 0.93	0.77	0.18	hedged possibility 0.75

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Original 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.

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The evidence of the UV-stable fixed point in non-perturbative regime has been found in the different short-distance regularization frameworks [ref] .

Cosmological $\Lambda$ driven inflation and produced massive particles · Introduction · 0.96

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These are ultimately expected to describe the evolution of geometry in discrete approaches to quantum gravity [ref] .

Models of Discrete Linear Evolution for Quantum Systems · Introduction · 0.87

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For the diagrams represented in Fig. [ref], using the mean-field approach ([ref]-[ref]) and indicating $[···]$ to be anti-clock like and $[···]^†$ clock like, we have [equation] where in the last line we use Eqs. (E1)-(E7) in Appendix E of Ref. [ref] .

Detailed discussions and calculations of quantum Regge calculus of Einstein-Cartan theory · Introduction · 0.97

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