期刊
LETTERS IN MATHEMATICAL PHYSICS
卷 104, 期 8, 页码 1003-1017出版社
SPRINGER
DOI: 10.1007/s11005-014-0699-9
关键词
group field theory; tensor models; large N limit
资金
- A. von Humboldt Stiftung through a Sofja Kovalevskaja Award
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 4-dimensional models of quantum gravity.
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