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

Abstract

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 $\mathbb{R}$-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.

27+7 pages; v2 closest to published version

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Cited by in corpus (10)

• Emergent Cosmology from Quantum Gravity in the Lorentzian Barrett-Crane Tensorial Group Field Theory Model
• Effective dynamics of scalar cosmological perturbations from quantum gravity
• Mean-field phase transitions in TGFT quantum gravity
• The Complete Barrett-Crane Model and its Causal Structure
• QFT with Tensorial and Local Degrees of Freedom: Phase Structure from Functional Renormalization
• Stochastic dynamics for Group Field Theories
• Quantum Gravity, Hydrodynamics and Emergent Cosmology: A Collection of Perspectives
• Scale invariance beyond criticality within the mean-field analysis of tensorial field theories
• Anomalous higher order Ward identities in tensorial group field theories without closure constraint
• Phase transitions in TGFT: Landau-Ginzburg analysis of the causally complete Lorentzian Barrett-Crane model