Melonic Phase Transition in Group Field Theory View Full Text


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Article Info

DATE

2014-08

AUTHORS

Aristide Baratin, Sylvain Carrozza, Daniele Oriti, James Ryan, Matteo Smerlak

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. More... »

PAGES

1003-1017

References to SciGraph publications

  • 1992-09. Counting colorful multi-dimensional trees in COMBINATORICA
  • 2012-06. Bubbles and jackets: new scaling bounds in topological group field theories in JOURNAL OF HIGH ENERGY PHYSICS
  • 2012-04. The Complete 1/N Expansion of Colored Tensor Models in Arbitrary Dimension in ANNALES HENRI POINCARÉ
  • 2014-09. Renormalization of a SU(2) Tensorial Group Field Theory in Three Dimensions in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2010-09. Bubble Divergences from Cellular Cohomology in LETTERS IN MATHEMATICAL PHYSICS
  • 2011-07. The 1/N Expansion of Colored Tensor Models in ANNALES HENRI POINCARÉ
  • 2014-04. Renormalization of Tensorial Group Field Theories: Abelian U(1) Models in Four Dimensions in COMMUNICATIONS IN MATHEMATICAL PHYSICS
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    URI

    http://scigraph.springernature.com/pub.10.1007/s11005-014-0699-9

    DOI

    http://dx.doi.org/10.1007/s11005-014-0699-9

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1050821701


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