Bubble divergences: sorting out topology from cell structure

Abstract

We conclude our analysis of bubble divergences in the flat spinfoam model. In [arXiv:1008.1476] we showed that the divergence degree of an arbitrary two-complex Gamma can be evaluated exactly by means of twisted cohomology. Here, we specialize this result to the case where Gamma is the two-skeleton of the cell decomposition of a pseudomanifold, and sharpen it with a careful analysis of the cellular and topological structures involved. Moreover, we explain in detail how this approach reproduces all the previous powercounting results for the Boulatov-Ooguri (colored) tensor models, and sheds light on algebraic-topological aspects of Gurau's 1/N expansion.

19 pages

References in corpus (3)

• The Ponzano-Regge model
• Scaling behaviour of three-dimensional group field theory
• Lost in Translation: Topological Singularities in Group Field Theory

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• Renormalization of Tensorial Group Field Theories: Abelian U(1) Models in Four Dimensions
• A new vacuum for Loop Quantum Gravity
• Group field theories for all loop quantum gravity
• Bounding bubbles: the vertex representation of 3d Group Field Theory and the suppression of pseudo-manifolds
• Holonomy spin foam models: Asymptotic geometry of the partition function
• Asymptotic safety in three-dimensional SU(2) Group Field Theory: evidence in the local potential approximation
• Quasi-local holographic dualities in non-perturbative 3d quantum gravity I - Convergence of multiple approaches and examples of Ponzano-Regge statistical duals
• Pachner moves in a 4d Riemannian holomorphic Spin Foam model
• Linking covariant and canonical LQG II: Spin foam projector
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• Group Field theory and Tensor Networks: towards a Ryu-Takayanagi formula in full quantum gravity
• Duality between Spin networks and the 2D Ising model
• Gauge symmetries in spinfoam gravity: the case for "cellular quantization"
• Infrared divergences in the EPRL-FK Spin Foam model
• Non-Perturbative 3D Quantum Gravity: Quantum Boundary States and Exact Partition Function
• Group Field Theory and Holographic Tensor Networks: Dynamical Corrections to the Ryu-Takayanagi formula
• Bulk amplitude and degree of divergence in 4d spin foams
• Numerical analysis of the self-energy in covariant Loop Quantum Gravity
• Renormalization of group field theories for quantum gravity: new scaling results and some suggestions
• Radiative corrections to the Lorentzian EPRL spin foam propagator
• A new realization of quantum geometry