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High Energy Physics - Theory, hep-th,General Relativity and Quantum Cosmology, gr-qc
Abstract:
Group field theories have recently been shown to admit a 1/N expansion
dominated by so-called `melonic graphs', dual to triangulated spheres. In this
note, we deepen the analysis of this melonic sector. We obtain a combinatorial
formula for the melonic amplitudes in terms of a graph polynomial related to a
higher dimensional generalization of the Kirchhoff tree-matrix theorem. Simple
bounds on these amplitudes show the existence of a phase transition driven by
melonic interaction processes. We restrict our study to the Boulatov-Ooguri
models, which describe topological BF theories and are the basis for the
construction of four dimensional models of quantum gravity.
