Generalised Amit-Roginsky model from perturbations of 3d quantum gravity

TL;DR

This paper derives a generalized Amit-Roginsky vector model from perturbations around classical solutions in 3d quantum gravity group field theory, linking quantum geometric models with tensorial models in flat space.

Contribution

It introduces a new generalized Amit-Roginsky model from 3d quantum gravity, establishing a potential unified framework between quantum geometric and tensorial models.

Findings

Derived a generalized Amit-Roginsky model from 3d quantum gravity perturbations.

Linked tensorial quantum field theories with models like SYK.

Showed how to recover the original Amit-Roginsky model through specific perturbations.

Abstract

A generalised Amit-Roginsky vector model in flat space is obtained as the effective dynamics of pertubations around a classical solution of the Boulatov group field theory for 3d euclidean quantum gravity, extended to include additional matter degrees of freedom. By further restricting the type of perturbations, the original Amit-Roginsky model can be obtained. This result suggests a general link (and possibly a unified framework) between two types of tensorial quantum field theories: quantum geometric group field theories and tensorial models for random geometry, on one hand, and melonic-dominated vector and tensorial models in flat space, such as the Amit-Roginsky model (and the SYK model), on the other hand.