Generalized Amit-Roginsky model from perturbations of 3D quantum gravity

A generalized 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; on one hand quantum geometric group field theories and tensorial models for random geometry, and on the other hand melonic-dominated vector and tensorial models in flat space, such as the Amit-Roginsky model and the Sachdev-Ye-Kitaev model.