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arXiv · 1307.5026

Melonic phase transition in group field theory

Aristide Baratin·Sylvain Carrozza·Daniele Oriti·James P. Ryan·Matteo Smerlak
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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.

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Aristide Baratin, Sylvain Carrozza, Daniele Oriti, James P. Ryan, Matteo Smerlak. 2014-06-09. Melonic phase transition in group field theory. https://doi.org/10.1007/s11005-014-0699-9

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