Rainbow tensor model with enhanced symmetry and extreme melonic dominance

TL;DR

The paper analyzes a rainbow tensor model where extreme color-symmetry enforces melonic dominance, dramatically simplifying the large-N limit to propagator dressing alone. It derives and discusses the nonlinear Schwinger-Dyson equations for dressed propagators, highlighting non-analytic, color-ratio-dependent behavior and potential wall-crossing. The work also outlines the role of Ward identities, possible Connes-Kreimer Hopf-algebra formulations, and the relevance of spectral-curve methods and AMM/EO recursion in tensor contexts. Together, these results illuminate a tractable yet rich structure in tensor models with implications for integrability, non-linear algebra, and connections to holography. However, many open questions remain about fully realizing these connections and their relevance to quantum gravity.

Abstract

We introduce and briefly analyze the rainbow tensor model where all planar diagrams are melonic. This leads to considerable simplification of the large N limit as compared to that of the matrix model: in particular, what are dressed in this limit are propagators only, which leads to an oversimplified closed set of Schwinger-Dyson equations for multi-point correlators. We briefly touch upon the Ward identities, the substitute of the spectral curve and the AMM/EO topological recursion and their possible connections to Connes-Kreimer theory and forest formulas.