Mean-field phase transitions in TGFT quantum gravity

Abstract

Controlling the continuum limit and extracting effective gravitational physics are shared challenges for quantum gravity approaches based on quantum discrete structures. The description of quantum gravity in terms of tensorial group field theory (TGFT) has recently led to much progress in its application to phenomenology, in particular cosmology. This application relies on the assumption of a phase transition to a nontrivial vacuum (condensate) state describable by mean-field theory, an assumption that is difficult to corroborate by a full renormalization group flow analysis due to the complexity of the relevant TGFT models. Here we demonstrate that this assumption is justified due to the specific ingredients of realistic quantum geometric TGFT models: combinatorially non-local interactions, matter degrees of freedom and Lorentz group data together with the encoding of micro-causality. This greatly strengthens the evidence for the existence of a meaningful continuum gravitational regime in group-field and spin-foam quantum gravity, the phenomenology of which is amenable to explicit computations in a mean-field approximation.

Revised version in line with the publication in PRL

References in corpus (10)

• Nonperturbative Quantum Gravity
• Random tensor models in the large N limit: Uncoloring the colored tensor models
• Group field theory with non-commutative metric variables
• Invitation to Random Tensors
• Critical behavior in spherical and hyperbolic spaces
• Group field theory condensate cosmology: An appetizer
• Emergent Cosmology from Quantum Gravity in the Lorentzian Barrett-Crane Tensorial Group Field Theory Model
• The Complete Barrett-Crane Model and its Causal Structure
• Phase transitions in TGFT: a Landau-Ginzburg analysis of Lorentzian quantum geometric models
• Non-commutative Fourier transform for the Lorentz group via the Duflo map

Cited by in corpus (11)

• Scalar Cosmological Perturbations from Quantum Entanglement within Lorentzian Quantum Gravity
• QFT with Tensorial and Local Degrees of Freedom: Phase Structure from Functional Renormalization
• Scalar Cosmological Perturbations from Quantum Gravitational Entanglement
• Generalised Gaussian states in group field theory and $\mathfrak{su}(1,1)$ quantum cosmology
• Relational dynamics and Page-Wootters formalism in group field theory
• Curvature from multipartite entanglement in quantum gravity states
• Hilbert space formalisms for group field theory
• Reconstructing the metric in group field theory
• Scale invariance beyond criticality within the mean-field analysis of tensorial field theories
• Quantum Gravity, Hydrodynamics and Emergent Cosmology: A Collection of Perspectives
• Phase transitions in TGFT: Landau-Ginzburg analysis of the causally complete Lorentzian Barrett-Crane model