No Ward-Takahashi identity violation for Abelian tensorial group field theories with a closure constraint

Vincent Lahoche (1) , Bêm-Biéri Barthélémy Natta , Dine Ousmane Samary (1)

1 LIST (CEA) - Laboratoire d'Intégration des Systèmes et des Technologies

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.

Mots clés: 71.70.Ej; 02.40.Gh; 03.65.-w; Renormalization group; group field theories; tensorial group field theories; tensor models; quantum gravity; random geometry; Ward-Takahashi identities; field theory: group; expansion: vertex; Ward-Takahashi identity; group: abelian; propagator; nonperturbative; renormalization group: flow; fixed point; model: tensor

Domaines: Physique des Hautes Energies - Théorie [hep-th]

Vincent Lahoche, Bêm-Biéri Barthélémy Natta, Dine Ousmane Samary. No Ward-Takahashi identity violation for Abelian tensorial group field theories with a closure constraint. Physical Review D, 2021, 104 (10), pp.106013. ⟨10.1103/PhysRevD.104.106013⟩. ⟨hal-03335450⟩