Most tensor field theories are known for admitting a large N expansion which is dominated by melonic graphs. This feature is shared with some vectori theories as in the SYK model, or the Amit-Roginsky (AR) model. In this talk, I will present how a generalized version of the AR model can be obtained as a perturbation around classical solutions of the Boulatov model, a tensorial field theory endowed with additional group data. After an overview of the main features of the Boulatov model and its equation of motions, I will give necessary conditions on the classical solution to recover an Amit-Roginsky-like model as a perturbation around this solution. This result exhibits how a vector model exhibiting a large N melonic limit can arise from a richer tensorial theory with similar features. This talk is based on a collaboration with A. Tanasa, D. Oriti, X. Pang and Y. Wang.
