Functional Renormalization Group analysis of rank 3 tensorial group field theory: The full quartic invariant truncation

TL;DR

This paper applies the functional renormalization group to a rank 3 tensorial group field theory, including all quartic interactions, revealing the importance of non-melonic and double-trace operators for accurate critical behavior analysis.

Contribution

It provides a comprehensive analysis of the full quartic invariant truncation, including non-melonic and double-trace interactions, highlighting their impact on critical exponents and renormalization group flow.

Findings

Inclusion of non-melonic operators affects scaling dimensions.

Double-trace operators significantly alter critical exponents.

Subtleties arise in assigning scaling dimensions to non-melonic sectors.

Abstract

In this paper we consider the complete momentum-independent quartic order truncation for the effective average action of a real Abelian rank 3 tensorial group field theory. This complete truncation includes non-melonic as well as double-trace interactions. In the usual functional renormalization group perspective, the inclusion of more operators that belong to the underlying theory space corresponds to an improvement of the truncation of the effective average action. We show that the inclusion of non-melonic and double-trace operators in the truncation brings subtleties. In particular, we discuss the assignment of scaling dimensions to the non-melonic sector and how the inclusion of double-trace operators considerably changes the results for critical exponents when they are not included. We argue that this is not a particular problem of the present model by comparing the results with a pure tensor model. We discuss how these issues should be investigated in future work.