Quantum mechanics

Theoretical physics

Functional renormalization group

Fixed point

Pure mathematics

Mathematical physics

Quantum field theory

Quantum gravity

Group theory

Field (mathematics)

Abelian group

Field theory (psychology)

Constraint (computer-aided design)

Thermal quantum field theory

Group field theory

Physics

Renormalization group

Mathematics

Quantum electrodynamics

Flow (mathematics)

Quartic function

Mathematical analysis

Geometry

Quantum

Mechanics

Group (periodic table)

Asymptotic safety in quantum gravity

Universe

This manuscript aims at giving our new advance on the functional renormalization group applied to tensorial group field theory. It is based on a series of our three papers [arXiv:1803.09902], [arXiv:1809.00247] and [arXiv:1809.06081]. We consider the polynomial Abelian $U(1)^d$ models without closure constraint, especially we discuss the case of quartic melonic interaction. We present a new approach to solve the exact Wetterich flow equation called the effective vertex expansion method, and investigate the resulting flow equations, especially about 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 phase transition into the reduced phase space given by the Ward constraint.

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