Bounding bubbles: The vertex representation of 3d group field theory and the suppression of pseudomanifolds

Sylvain Carrozza and Daniele Oriti
Phys. Rev. D 85, 044004 – Published 3 February 2012

Abstract

Based on recent work on simplicial diffeomorphisms in colored group field theories, we develop a representation of the colored Boulatov model, in which the group field theory (GFT) fields depend on variables associated to vertices of the associated simplicial complex, as opposed to edges. On top of simplifying the action of diffeomorphisms, the main advantage of this representation is that the GFT Feynman graphs have a different stranded structure, which allows a direct identification of subgraphs associated to bubbles, and their evaluation is simplified drastically. As a first important application of this formulation, we derive new scaling bounds for the regularized amplitudes, organized in terms of the genera of the bubbles, and show how the pseudomanifold configurations appearing in the perturbative expansion are suppressed as compared to manifolds. Moreover, these bounds are proved to be optimal.

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  • Received 26 November 2011

DOI:https://doi.org/10.1103/PhysRevD.85.044004

© 2012 American Physical Society

Authors & Affiliations

Sylvain Carrozza1,2,* and Daniele Oriti1,†

  • 1Max Planck Institute for Gravitational Physics, Albert Einstein Institute, Am Mühlenberg 1, 14476 Golm, Germany, EU
  • 2Laboratoire de Physique Théorique, CNRS UMR 8627, Université Paris XI, F-91405 Orsay Cedex, France, EU

  • *sylvain.carrozza@aei.mpg.de
  • daniele.oriti@aei.mpg.de

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Vol. 85, Iss. 4 — 15 February 2012

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