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Group field theory as the microscopic description of the quantum spacetime fluid: a new perspective on the continuum in quantum gravity

Daniele Oriti

TL;DR

This paper proposes group field theory (GFT) as a unifying, non-perturbative framework for quantum gravity that subsumes loop quantum gravity, spin foams, and simplicial approaches. It advocates viewing quantum spacetime as a condensed-matter system in which continuum geometry emerges in a many-particle, near-equilibrium phase, potentially as a Bose-Einstein condensate of GFT quanta. The authors discuss how existing continuum-emergence strategies from LQG/SF, quantum Regge calculus, and dynamical triangulations translate into GFT language, and argue for a shift toward hydrodynamic, phase-structure analyses to access the continuum. They sketch a concrete program around geometrogenesis and BE condensates to derive effective spacetime dynamics from microscopic GFT dynamics, aiming to recover General Relativity or its quantum-corrected counterpart in the continuum limit.

Abstract

We introduce the group field theory (GFT) formalism for non-perturbative quantum gravity, and present it as a potential unifying framework for several other quantum gravity approaches, i.e. loop quantum gravity and simplicial quantum gravity ones. We then argue in favor of and present in detail what we believe is a new GFT perspective on the emergence of continuum spacetime from discrete quantum structures, based on the idea of quantum space as a condensed matter system. We put forward a more specific, albeit still very much tentative, proposal for the relevant phase of the GFT corresponding to the continuum: a Bose-Einstein condensate of GFT quanta. Finally, we sketch how the proposal may be realised and its effective dynamics could be extracted in the GFT setting and compared with continuum gravity theories.

Group field theory as the microscopic description of the quantum spacetime fluid: a new perspective on the continuum in quantum gravity

TL;DR

This paper proposes group field theory (GFT) as a unifying, non-perturbative framework for quantum gravity that subsumes loop quantum gravity, spin foams, and simplicial approaches. It advocates viewing quantum spacetime as a condensed-matter system in which continuum geometry emerges in a many-particle, near-equilibrium phase, potentially as a Bose-Einstein condensate of GFT quanta. The authors discuss how existing continuum-emergence strategies from LQG/SF, quantum Regge calculus, and dynamical triangulations translate into GFT language, and argue for a shift toward hydrodynamic, phase-structure analyses to access the continuum. They sketch a concrete program around geometrogenesis and BE condensates to derive effective spacetime dynamics from microscopic GFT dynamics, aiming to recover General Relativity or its quantum-corrected counterpart in the continuum limit.

Abstract

We introduce the group field theory (GFT) formalism for non-perturbative quantum gravity, and present it as a potential unifying framework for several other quantum gravity approaches, i.e. loop quantum gravity and simplicial quantum gravity ones. We then argue in favor of and present in detail what we believe is a new GFT perspective on the emergence of continuum spacetime from discrete quantum structures, based on the idea of quantum space as a condensed matter system. We put forward a more specific, albeit still very much tentative, proposal for the relevant phase of the GFT corresponding to the continuum: a Bose-Einstein condensate of GFT quanta. Finally, we sketch how the proposal may be realised and its effective dynamics could be extracted in the GFT setting and compared with continuum gravity theories.

Paper Structure

This paper contains 29 sections, 20 equations, 4 figures.

Table of Contents

  1. Introduction
  2. The group field theory formalism
  3. Kinematics: the fundamental building blocks of quantum space
  4. Dynamics: the interaction and evolution of the atoms of space
  5. A peculiar quantum field theory (still, a proper field theory!)
  6. Group field theory as a common framework for discrete quantum gravity
  7. Convergence of formalisms, structures and languages
  8. Loop quantum gravity and group field theory
  9. Simplicial quantum gravity and group field theory
  10. Cui prodest?
  11. Building up a coherent picture of quantum spacetime
  12. Insights from loop quantum gravity and spin foam models
  13. Insights from quantum Regge calculus
  14. Insights from matrix models and dynamical triangulations
  15. The problem of the continuum: current strategies from a GFT perspective
  16. ...and 14 more sections

Figures (4)

  • Figure 1: For the $D=3$ case, the association of a field with a 2-simplex, or equivalently its dual vertex, and of its arguments with the 1-faces of it, or equivalently with the links incident to the vertex, together with the labelling by group-theoretic variables.
  • Figure 2: A ' 2-particle state' (again, in the D=3 example)
  • Figure 3: The basic building blocks of the GFT Feynman diagrams (for $D=3$).
  • Figure 4: The gluing of vertices of interaction through propagators, again in the D=3 example. The rectangles represent the additional integrations imposing gauge invariance under the action of $G$, while the ellipses represent the implicit sum over permutations of the (labels of the) strands to be glued.