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

TL;DR

This paper analyzes radiative corrections in the Boulatov-Ooguri tensor model to the 2-point function, addressing how renormalization manifests when summing over spacetime topologies. Using heat-kernel regularization, gauge fixing, and saddle-point localization on flat connections, the authors identify a leading mass renormalization and a divergent term proportional to second derivatives of the propagator that cannot be absorbed by the original action. They argue that a consistent renormalization requires augmenting the kinetic term with Laplacian-type operators (e.g., a sum of Laplacians over the D strands) and develop a framework to study arbitrary 2-point graphs, including simply connected cases where the amplitude expands in derivatives of the bare propagator with potentially unbounded higher-derivative divergences. The work outlines a path toward a scale analysis and renormalization program for group field theories, highlighting the need for revised kinetic terms and a refined locality principle to achieve a renormalizable GFT framework.

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.

Figures (3)

• Figure 1: $D$ dimensional model propagator and vertex.
• Figure 2: 3d model propagator and vertex.
• Figure 3: 2-point function.

Theorems & Definitions (3)

• Lemma 1
• Lemma 2
• Lemma 3