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Critical behavior of colored tensor models in the large N limit
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Random tensor models in the large N limit: Uncoloring the colored tensor models
Tensor models generalize random matrix models in yielding a theory of dynamical triangulations in arbitrary dimensions. Colored tensor models have been shown to admit a 1/N expansion and a continuum…
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Diagrammatics of a colored SYK model and of an SYK-like tensor model, leading and next-to-leading orders
The Sachdev-Ye-Kitaev (SYK) model is a model of q interacting fermions. Gross and Rosenhaus have proposed a generalization of the SYK model which involves fermions with different flavors. In terms of…
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Radiative Corrections in the Boulatov-Ooguri Tensor Model: The 2-Point Function
The Boulatov-Ooguri tensor model generates a sum over spacetime topologies for the D-dimensional BF theory. We study here the quantum corrections to the propagator of the theory. In particular, we…
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Spin foam models for quantum gravity from lattice path integrals
Spin foam models for quantum gravity are derived from lattice path integrals. The setting involves variables from both lattice BF theory and Regge calculus. The action consists in a Regge action,…
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A Immirzi-like parameter for 3D quantum gravity
We study an Immirzi-like ambiguity in three-dimensional quantum gravity. It shares some features with the Immirzi parameter of four-dimensional loop quantum gravity: it does not affect the equations…
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Recurrence relations for spin foam vertices
We study recurrence relations for various Wigner 3nj-symbols and the non-topological 10j-symbol. For the 6j- and the 15j-symbols which correspond to basic amplitudes of 3d and 4d topological spin…
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Bubble Divergences from Cellular Cohomology
We consider a class of lattice topological field theories, among which are the weak-coupling limit of 2d Yang–Mills theory, the Ponzano–Regge model of 3d quantum gravity and discrete BF theory, whose…
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The Hamiltonian constraint in 3d Riemannian loop quantum gravity
We discretize the Hamiltonian scalar constraint of three-dimensional Riemannian gravity on a graph of the loop quantum gravity phase space. This Hamiltonian has a clear interpretation in terms of…
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Towards the Turaev-Viro amplitudes from a Hamiltonian constraint
3D Loop Quantum Gravity with a vanishing cosmological constant can be related to the quantization of the $\textrm{SU}(2)$ BF theory discretized on a lattice. At the classical level, this discrete…
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