Phase transitions in tensorial group field theories: Landau-Ginzburg analysis of models with both local and non-local degrees of freedom

A bstract In the tensorial group field theory approach to quantum gravity, the theory is based on discrete building blocks and continuum spacetime is expected to emerge from their collective dynamics, possibly at criticality, via a phase transition. On a compact group of fixed volume this can be exp...

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Bibliographic Details
Published in:The journal of high energy physics 2021-12, Vol.2021 (12), p.1-35, Article 201
Main Authors: Marchetti, Luca, Oriti, Daniele, Pithis, Andreas G. A., Thürigen, Johannes
Format: Article
Language:English
Subjects:
Classical and Quantum Gravitation
Degrees of freedom
Elementary Particles
High energy physics
Lattice Models of Gravity
Lie groups
Mean field theory
Models of Quantum Gravity
Nonperturbative Effects
Phase transitions
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum gravity
Quantum Physics
Regular Article - Theoretical Physics
Relativity
Relativity Theory
Renormalization Group
Scalars
Spacetime
String Theory
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Summary:A bstract In the tensorial group field theory approach to quantum gravity, the theory is based on discrete building blocks and continuum spacetime is expected to emerge from their collective dynamics, possibly at criticality, via a phase transition. On a compact group of fixed volume this can be expected to be only possible in a large-volume or thermodynamic limit. Here we show how phase transitions are possible in TGFTs in two cases: a) considering the non-local group degrees of freedom on a non-compact Lie group instead of a compact one (or taking a large-volume limit of a compact group); b) in models including ℝ-valued local degrees of freedom (that can be interpreted as discrete scalar fields, often used in this context to provide a matter reference frame). After adapting the Landau-Ginzburg approach to this setting of mixed local/non-local degrees of freedom, we determine the critical dimension beyond which there is a Gaussian fixed point and a continuous phase transition which can be described by mean-field theory. This is an important step towards the realization of a phase transition to continuum spacetime in realistic TGFT models for quantum gravity.
ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP12(2021)201