Radiative corrections in the Boulatov-Ooguri tensor model: The 2-point function

TL;DR

This paper investigates quantum radiative corrections in the Boulatov-Ooguri tensor model, revealing a mass renormalization and an uncounterable divergence in the propagator at second order, impacting the model's renormalization properties.

Contribution

It provides the first detailed analysis of second-order quantum corrections in the Boulatov-Ooguri tensor model, highlighting issues with wave-function renormalization.

Findings

Second-order corrections induce mass renormalization.

A divergence appears that cannot be canceled by initial action counter-terms.

The divergence suggests challenges in the model's renormalizability.

Abstract

The Boulatov-Ooguri tensor model generates a sum over spacetime topologies for the $D$-dimensional BF theory. We study here the quantum corrections to the propagator of the theory. In particular, we find that the radiative corrections at the second order in the coupling constant yield a mass renormalization. They also exhibit a divergence which cannot be balanced with a counter-term in the initial action, and which usually corresponds to the wave-function renormalization.