Bulk amplitude and degree of divergence in 4d spin foams

Abstract

We study the 4-d holomorphic Spin Foam amplitude on arbitrary connected 2-complexes and degrees of divergence. With recently developed tools and truncation scheme, we derive a formula for a certain class of graphs, which allows us to write down the value of bulk amplitudes simply based on graph properties. We then generalize the result to arbitrary connected 2-complexes and extract a simple expression for the degree of divergence only in terms of combinatorial properties and topological invariants. The distinct behaviors of the model in different regions of parameter space signal phase transitions. In the regime which is of physical interest for recovering diffeomorphsim symmetry in the continuum limit, the most divergent configurations are melonic graphs. We end with a discussion of physical implications.

25+7 pages, 10 figures

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Cited by in corpus (12)

• Towards a phase diagram for spin foams
• Coarse graining flow of spin foam intertwiners
• Renormalizable Group Field Theory beyond melonic diagrams: an example in rank four
• Quantum gravity kinematics from extended TQFTs
• Semiclassical Limit of New Path Integral Formulation from Reduced Phase Space Loop Quantum Gravity
• From spin foams to area metric dynamics to gravitons
• Renormalization of group field theories for quantum gravity: new scaling results and some suggestions
• Spikes and spines in 4D Lorentzian simplicial quantum gravity
• Area Propagator and Boosted Spin Networks in Loop Quantum Gravity
• Modified Graviton Dynamics From Spin Foams: The Area Regge Action
• A Model of Spinfoam Coupled with an Environment
• 3D Quantum Gravity from Holomorphic Blocks