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The Schwinger-Dyson Equations (SDEs) of matrix models are known to form(half) a Virasoro algebra and have become a standard tool to solve matrixmodels. The algebra generated by SDEs in tensor models (for random tensors in asuitable ensemble) is a specific generalization of the Virasoro algebra and itis important to show that these new symmetries determine the physicalsolutions. We prove this result for random tensors at large N. Compared tomatrix models, tensor models have more than a single invariant at each order inthe tensor entries and the SDEs make them proliferate. However, the specificcombinatorics of the dominant observables allows to restrict to linear SDEs andwe show that they determine a unique physical perturbative solution. This givesa new proof that tensor models are Gaussian at large N, with the covariancebeing the full 2-point function.

Revisiting random tensor models at large N via the Schwinger-Dyson equations