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Functional Renormalization Group analysis of rank 3 tensorial group field theory: The full quartic invariant truncation

By Joseph Ben Geloun, Tim A. Koslowski, Daniele Oriti and Antonio D. Pereira

Abstract

International audienceIn this paper, we consider the complete momentum-independent quartic order truncation for the effective average action of a real Abelian rank-3 tensorial group field theory. This complete truncation includes nonmelonic as well as double-trace interactions. In the usual functional renormalization group perspective, the inclusion of more operators that belong to the underlying theory space corresponds to an improvement of the truncation of the effective average action. We show that the inclusion of nonmelonic and double-trace operators in the truncation brings subtleties. In particular, we discuss the assignment of scaling dimensions to the nonmelonic sector and how the inclusion of double-trace operators considerably changes the results for critical exponents with respect to those obtained when they are not included. We argue that this is not a particular problem of the present model by comparing the results with a pure tensor model. We discuss how these issues should be investigated in future work

Topics: functional analysis, renormalization group, effective field theory, higher-order: 3, model: tensor, field theory: group, 11.10.Gh, scaling: dimension, 04.60.Pp, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], [PHYS.GRQC]Physics [physics]/General Relativity and Quantum Cosmology [gr-qc]
Publisher: 'American Physical Society (APS)'
Year: 2018
DOI identifier: 10.1103/PhysRevD.97.126018
OAI identifier: oai:HAL:hal-01797123v1
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