Coarse graining methods for spin net and spin foam models

Abstract

We undertake first steps in making a class of discrete models of quantum gravity, spin foams, accessible to a large scale analysis by numerical and computational methods. In particular, we apply Migdal-Kadanoff and Tensor Network Renormalization schemes to spin net and spin foam models based on finite Abelian groups and introduce `cutoff models' to probe the fate of gauge symmetries under various such approximated renormalization group flows. For the Tensor Network Renormalization analysis, a new Gauss constraint preserving algorithm is introduced to improve numerical stability and aid physical interpretation. We also describe the fixed point structure and establish an equivalence of certain models.

39 pages, 13 figures, 1 table

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Cited by in corpus (65)

• The Spin Foam Approach to Quantum Gravity
• Tensor Network Renormalization
• Colored Tensor Models - a Review
• Group field theory and simplicial gravity path integrals: A model for Holst-Plebanski gravity
• Tensor Networks for Lattice Gauge Theories with continuous groups
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• Tensorial methods and renormalization in Group Field Theories
• Decorated tensor network renormalization for lattice gauge theories and spin foam models
• Algorithms for tensor network renormalization
• From the discrete to the continuous - towards a cylindrically consistent dynamics
• Fusion basis for lattice gauge theory and loop quantum gravity
• Emergent Models for Gravity: an Overview of Microscopic Models
• A new vacuum for Loop Quantum Gravity
• Holonomy Spin Foam Models: Definition and Coarse Graining
• Effective Spin Foam Models for Lorentzian Quantum Gravity
• Functional Renormalisation Group analysis of Tensorial Group Field Theories on ${\mathbb{R}}^d$
• Path integral measure and triangulation independence in discrete gravity
• Towards a phase diagram for spin foams
• Hypercuboidal renormalization in spin foam quantum gravity
• Functional Renormalisation Group analysis of a Tensorial Group Field Theory on ${\mathbb{R}}^3$
• Investigation of the Spinfoam Path integral with Quantum Cuboid Intertwiners
• Coarse graining flow of spin foam intertwiners
• Observational Exclusion of a Consistent Quantum Cosmology Scenario
• Generalized quantum gravity condensates for homogeneous geometries and cosmology
• Group field theory condensate cosmology: An appetizer
• Quantum group spin nets: refinement limit and relation to spin foams
• Renormalization of symmetry restricted spin foam models with curvature in the asymptotic regime
• Renormalization of an Abelian Tensor Group Field Theory: Solution at Leading Order
• Discrete gravity dynamics from effective spin foams
• Towards the Turaev-Viro amplitudes from a Hamiltonian constraint
• Pachner moves in a 4d Riemannian holomorphic Spin Foam model
• Bubble divergences and gauge symmetries in spin foams
• Three-dimensional finite temperature Z${}_2$ gauge theory with tensor network scheme
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• New Hamiltonians for loop quantum cosmology with arbitrary spin representations
• Hyper-optimized approximate contraction of tensor networks with arbitrary geometry
• From spin foams to area metric dynamics to gravitons
• Emergence of Spacetime in a restricted Spin-foam model
• Discretisations, Constraints and Diffeomorphisms in Quantum Gravity
• Group Field Theory and Holographic Tensor Networks: Dynamical Corrections to the Ryu-Takayanagi formula
• Holonomy Spin Foam Models: Boundary Hilbert spaces and Time Evolution Operators
• Ryu-Takayanagi Formula for Symmetric Random Tensor Networks
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• A Monte Carlo algorithm for spin foam intertwiners
• Generating Functionals for Spin Foam Amplitudes
• Can quantum gravity be both consistent and complete?
• Aspects of quantum gravity
• Perfect discretization of path integrals