Renormalization of an Abelian Tensor Group Field Theory: Solution at Leading 
Order

Lahoche, Vincent; Oriti, Daniele; Rivasseau, Vincent

doi:10.1007/JHEP04(2015)095

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Renormalization of an Abelian Tensor Group Field Theory: Solution at Leading Order

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Oriti, Daniele
Microscopic Quantum Structure & Dynamics of Spacetime, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Lahoche, V., Oriti, D., & Rivasseau, V. (2015). Renormalization of an Abelian Tensor Group Field Theory: Solution at Leading Order. Journal of high energy physics: JHEP, 2015(04): 095. doi:10.1007/JHEP04(2015)095.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0024-D430-2

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.