Abstract
This paper aims at investigating the nonperturbative functional renormalization group for tensorial group field theories with nontrivial kinetic action and closure constraint. We consider the quartic melonic just-renormalizable $[U(1){]}^{6}$ model and show that due to this closure constraint the first order Ward-Takahashi identity takes the trivial form as for the models with propagators proportional to identity. We then construct the new version of the effective vertex expansion applicable to this class of models, which in particular allows us to close the hierarchical structure of the flow equations in the melonic sector. As a consequence, there are no additional constraints on the flow equations, and then we can focus on the existence of the physical Wilson-Fisher fixed-points in the symmetric phase.
Highlights
The quantum theory of gravitation or quantum gravity (QG), aiming to provide a unification between general relativity and quantum physics, is probably one of the major challenges of the century
In this manuscript we intend to respond to this assertion, i.e., we investigate the compatibility with WT identities and the functional renormalization group (FRG) solutions for Uð1Þ-models and provide the argument in favor of this Gauss constraint for emergent quantum gravity models
We investigated a nonperturbative solution of the exact RG equation for a rank-6 TGFT with a closure constraint
Summary
The quantum theory of gravitation or quantum gravity (QG), aiming to provide a unification between general relativity and quantum physics, is probably one of the major challenges of the century. They assume the idea that a special kind of invariance is required to make the theory power-countable The existence of such a power counting in turn is the basic ingredient to define a renormalization group flow, suitable to describe large scale physics and phase transitions [14–52]. We considered only models without Gauss closure constraint and we have already suspected that this closure constraint could make the Ward constraint obsolete, that is to say without effect on the Wetterich flow equations In this manuscript we intend to respond to this assertion, i.e., we investigate the compatibility with WT identities and the functional renormalization group (FRG) solutions for Uð1Þ-models and provide the argument in favor of this Gauss constraint for emergent quantum gravity models. We give some Appendixes to elucidate the detailed computations using throughout the manuscript
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