Functional renormalization group for the $U(1)$-$T_5^6$ tensorial group field theory with closure constraint

TL;DR

This paper applies the functional renormalization group to a $U(1)$ tensor field theory with closure constraint, deriving flow equations, analyzing fixed points, and exploring the theory's UV behavior and potential asymptotic safety.

Contribution

It derives the flow equations for the $T_5^6$ tensor model with closure constraint and investigates its fixed points and UV completion, revealing signs of asymptotic safety.

Findings

The theory is nonasymptotically free.

Existence of several nontrivial fixed points.

Evidence supporting asymptotic safety.

Abstract

This paper is focused on the functional renormalization group applied to the $T_5^6$ tensor model on the Abelian group $U(1)$ with closure constraint. For the first time, we derive the flow equations for the couplings and mass parameters in a suitable truncation around the marginal interactions with respect to the perturbative power counting. For the second time, we study the behavior around the Gaussian fixed point, and show that the theory is nonasymptotically free. Finally, we discuss the UV completion of the theory. We show the existence of several nontrivial fixed points, study the behavior of the renormalization group flow around them, and point out evidence in favor of an asymptotically safe theory.