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Mean-Field Phase Transitions in Tensorial Group Field Theory Quantum Gravity.
Luca Marchetti1, Daniele Oriti1,2, Andreas G A Pithis1,2
1Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität München, Theresienstr. 37, 80333 München, Germany.
Physical Review Letters
|April 21, 2023
Summary
This study justifies the mean-field approximation for tensorial group field theory (TGFT) in quantum gravity. Realistic TGFT models support a phase transition to a non-trivial vacuum, enabling effective gravitational physics computations.
Area of Science:
- Quantum Gravity
- Theoretical Physics
- Cosmology
Background:
- Controlling continuum limits and extracting effective gravitational physics are key challenges in quantum gravity.
- Tensorial Group Field Theory (TGFT) offers a promising framework for quantum gravity, with recent progress in cosmological applications.
- Phenomenological applications of TGFT often rely on mean-field theory assumptions for phase transitions to a non-trivial vacuum, which are hard to verify with full RG flow analysis.
Purpose of the Study:
- To demonstrate the validity of the mean-field approximation assumption in realistic quantum geometric TGFT models.
- To strengthen the evidence for a meaningful continuum gravitational regime in TGFT and related quantum gravity approaches.
- To support the explicit computation of phenomenological aspects of quantum gravity using mean-field approximations.
Main Methods:
- Analysis of realistic quantum geometric TGFT models.
- Investigation of key model ingredients: combinatorially nonlocal interactions, matter degrees of freedom, Lorentz group data, and microcausality.
- Justification of the mean-field theory assumption for vacuum condensate states.
Main Results:
- The assumption of a phase transition to a non-trivial vacuum (condensate) in TGFT is justified.
- Specific ingredients of realistic TGFT models (nonlocal interactions, matter, Lorentz data, microcausality) support the mean-field approximation.
- Evidence for a meaningful continuum gravitational regime in group-field and spin-foam quantum gravity is significantly strengthened.
Conclusions:
- The mean-field approximation is a valid approach for studying the phenomenology of quantum gravity within realistic TGFT models.
- Explicit computations of quantum gravity phenomenology are feasible using mean-field approximations in TGFT.
- This work enhances the prospects for connecting discrete quantum gravity structures to observable gravitational physics.
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