Article Dans Une Revue Letters in Mathematical Physics Année : 2014

Melonic phase transition in group field theory

Résumé

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.

Dates et versions

hal-01116631 , version 1 (13-02-2015)

Identifiants

Citer

Aristide Baratin, Sylvain Carrozza, Daniele Oriti, James P. Ryan, Matteo Smerlak. Melonic phase transition in group field theory. Letters in Mathematical Physics, 2014, 104 (8), pp.10.1007/s11005-014-0699-9. ⟨10.1007/s11005-014-0699-9⟩. ⟨hal-01116631⟩
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