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Mean-field phase transitions in TGFT quantum gravity

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arxiv 2211.12768 v2 pith:5QEO5YEF submitted 2022-11-23 gr-qc hep-th

Luca Marchetti , Daniele Oriti , Andreas G. A. Pithis , Johannes Thürigen This is my paper · ORCID
classification gr-qchep-th
keywords quantumgravitytgftassumptiongroupmean-fieldapplicationcontinuum
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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.

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Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Relational Observables in Group Field Theory

    gr-qc 2024-12 conditional novelty 7.0 of 10

    POVM-based conditioning on scalar-field quantum reference frames defines relational observables in group field theory that match prior number and volume results on coherent states.

  2. Multiple-Order Tensor Field Theory: Enumeration of unitary invariant observables

    math-ph 2025-05 conditional novelty 6.0 of 10

    A Burnside-based enumeration formula, Theorem 4, counts unitary invariant tensor contractions built from fields of multiple orders, recovers known fixed-order counts as a special case, and generates new integer sequences.

  3. A state sum for four-dimensional Lorentzian quantum geometry in terms of edge vectors

    gr-qc 2025-01 conditional novelty 6.0 of 10

    A new state sum model for 4D Lorentzian quantum gravity is constructed from quantum edge vectors and related to the Barrett-Crane spin foam model.

  4. Quantum Gravity, Hydrodynamics and Emergent Cosmology: A Collection of Perspectives

    gr-qc 2024-11 unverdicted novelty 4.0 of 10

    The paper argues that an effective 'hydrodynamics on superspace' framework, realized in TGFT condensate cosmology, can unify quantum gravity and cosmology.

  5. Hilbert space formalisms for group field theory

    gr-qc 2024-12 accept novelty 3.0 of 10

    A structured review of the three main Hilbert space formalisms for group field theory, with emphasis on their assumptions and conceptual connections.

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