Renormalization of an Abelian tensor group field theory: solution at leading order

Lahoche, Vincent (LPT-UMR 8627, Université Paris 11, 91405, Orsay Cedex, France) ; Oriti, Daniele (0000 0001 0790 4262, Max Planck Institute for Gravitational Physics, Albert Einstein Institute, Am Mühlenberg 1, 14476, Potsdam, Germany) ; Rivasseau, Vincent (Laboratoire de physique théorique, UMR 8627, Université Paris 11, 91405, Orsay Cedex, France) (0000 0000 8658 0851, Perimeter Institute for Theoretical Physics, 31 Caroline St. N, N2L 2Y5, Waterloo, ON, Canada)

25 April 2015

Abstract: We study a just-renormalizable tensorial group field theory of rank six with quartic melonic interactions and Abelian group U(1). We introduce the formalism of the intermediate field, which allows a precise characterization of the leading order Feynman graphs. We define the renormalization of the model, compute its (perturbative) renormalization group flow and write its expansion in terms of effective couplings. We then establish closed equations for the two point and four point functions at leading (melonic) order. Using the effective expansion and its uniform exponential bounds we prove that these equations admit a unique solution at small renormalized coupling.

Published in: JHEP 1504 (2015) 095
Published by: Springer/SISSA
DOI: 10.1007/JHEP04(2015)095
arXiv: 1501.02086v2
License: CC-BY-4.0

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