Bounding bubbles: the vertex representation of 3d Group Field Theory and the suppression of pseudo-manifolds

Abstract

Based on recent work on simplicial diffeomorphisms in colored group field theories, we develop a representation of the colored Boulatov model, in which the GFT fields depend on variables associated to vertices of the associated simplicial complex, as opposed to edges. On top of simplifying the action of diffeomorphisms, the main advantage of this representation is that the GFT Feynman graphs have a different stranded structure, which allows a direct identification of subgraphs associated to bubbles, and their evaluation is simplified drastically. As a first important application of this formulation, we derive new scaling bounds for the regularized amplitudes, organized in terms of the genera of the bubbles, and show how the pseudo-manifolds configurations appearing in the perturbative expansion are suppressed as compared to manifolds. Moreover, these bounds are proved to be optimal.

28 pages, 17 figures. Few typos fixed. Minor corrections in figure 6 and theorem 2

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Cited by in corpus (22)

• Colored Tensor Models - a Review
• Random tensor models in the large N limit: Uncoloring the colored tensor models
• Renormalization of an SU(2) Tensorial Group Field Theory in Three Dimensions
• A generalization of the Virasoro algebra to arbitrary dimensions
• Tensorial methods and renormalization in Group Field Theories
• Coarse graining methods for spin net and spin foam models
• The 1/N Expansion of Tensor Models Beyond Perturbation Theory
• Renormalization of Tensorial Group Field Theories: Abelian U(1) Models in Four Dimensions
• Flowing in Group Field Theory Space: a Review
• Phase Transition in Dually Weighted Colored Tensor Models
• The Schwinger Dyson equations and the algebra of constraints of random tensor models at all orders
• Invitation to Random Tensors
• Canonical tensor models with local time
• Uniqueness of canonical tensor model with local time
• Super tensor models, super fuzzy spaces and super n-ary transformations
• Bulk amplitude and degree of divergence in 4d spin foams
• Gravity as an emergent phenomenon: a GFT perspective
• On the depth of quantum space
• On the space of generalized fluxes for loop quantum gravity
• Weighting bubbles in group field theory
• Transition Amplitudes in 3D Quantum Gravity: Boundaries and Holography in the Coloured Boulatov Model
• From Dimensional Reduction of 4d Spin Foam Model to Adding Non-Gravitational Fields to 3d Spin Foam Model