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.
Highlights
Attempts to quantize the gravitational field started soon after the very formulation of General Relativity and of quantum field theory [1]
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
While suggestions that a more radical departure from standard spacetime-based physics were voiced, the first strategy was to apply to the gravitational field the same techniques that have been successfully applied to other interactions, turning General Relativity into a quantum field theory
Summary
Attempts to quantize the gravitational field started soon after the very formulation of General Relativity (the current classical theory of the gravitational field) and of quantum field theory (the modern framework for describing fundamental interactions) [1]. They are a class of quantum field theories where, at the same time, one tries to apply standard field-theoretic techniques familiar from the theory of fundamental interactions and is forced to modify, adapt, and sometimes drop several of them, due to the peculiar spacetime-free setting They incarnate a very different perspective on quantum gravity, with respect to other approaches mentioned above and based on the wish for a straightforward quantization of General Relativity, while managing to incorporate several of their defining structures and being historically a further development of them. We find that the extension of the truncation to nonmelonic diagrams does not lead, in most cases, to drastic changes in the flow, while the effects of the disconnected diagrams can be more profound, calling for a careful consideration of their role in TGFTs
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