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

Understand

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.