Next Article in Journal
A Post-Newtonian Gravitomagnetic Effect on the Orbital Motion of a Test Particle around Its Primary Induced by the Spin of a Distant Third Body
Next Article in Special Issue
Reconstruction of Mimetic Gravity in a Non-Singular Bouncing Universe from Quantum Gravity
Previous Article in Journal
Anti-Newtonian Expansions and the Functional Renormalization Group
Previous Article in Special Issue
Status of Background-Independent Coarse Graining in Tensor Models for Quantum Gravity
Open AccessReview

Progress in Solving the Nonperturbative Renormalization Group for Tensorial Group Field Theory

Commissariat à l’Énergie Atomique (CEA, LIST), 8 Avenue de la Vauve, 91120 Palaiseau, France
Faculté des Sciences et Techniques/ICMPA-UNESCO Chair, Université d’Abomey-Calavi, Cotonou 072 BP 50, Benin
Authors to whom correspondence should be addressed.
Universe 2019, 5(3), 86;
Received: 12 December 2018 / Revised: 16 March 2019 / Accepted: 18 March 2019 / Published: 26 March 2019
(This article belongs to the Special Issue Progress in Group Field Theory and Related Quantum Gravity Formalisms)
This manuscript aims at giving new advances on the functional renormalization group applied to the tensorial group field theory. It is based on the series of our three papers (Lahoche, et al., Class. Quantum Gravity 2018, 35, 19), (Lahoche, et al., Phys. Rev. D 2018, 98, 126010) and (Lahoche, et al., Nucl. Phys. B, 2019, 940, 190–213). We consider the polynomial Abelian U ( 1 ) d models without the closure constraint. More specifically, we discuss the case of the quartic melonic interaction. We present a new approach, namely the effective vertex expansion method, to solve the exact Wetterich flow equation and investigate the resulting flow equations, especially regarding the existence of non-Gaussian fixed points for their connection with phase transitions. To complete this method, we consider a non-trivial constraint arising from the Ward–Takahashi identities and discuss the disappearance of the global non-trivial fixed points taking into account this constraint. Finally, we argue in favor of an alternative scenario involving a first order phase transition into the reduced phase space given by the Ward constraint. View Full-Text
Keywords: nonperturbative renormalization group; quantum gravity; random geometry nonperturbative renormalization group; quantum gravity; random geometry
Show Figures

Figure 1

MDPI and ACS Style

Lahoche, V.; Ousmane Samary, D. Progress in Solving the Nonperturbative Renormalization Group for Tensorial Group Field Theory. Universe 2019, 5, 86.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

Back to TopTop