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Letters in Mathematical Physics

, Volume 104, Issue 8, pp 1003–1017 | Cite as

Melonic Phase Transition in Group Field Theory

  • Aristide BaratinEmail author
  • Sylvain Carrozza
  • Daniele Oriti
  • James Ryan
  • Matteo Smerlak
Article

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 4-dimensional models of quantum gravity.

Mathematics Subject Classification

Primary 81T25 83C27 Secondary 83C45 

Keywords

group field theory tensor models large N limit 

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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Aristide Baratin
    • 1
    Email author
  • Sylvain Carrozza
    • 1
  • Daniele Oriti
    • 1
  • James Ryan
    • 1
  • Matteo Smerlak
    • 1
  1. 1.Max-Planck-Institut für GravitationsphysikGolmGermany

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