Redundant moments of non-melonic random tensor models: simplifying the tensor bootstrap

Abstract

We prove the redundancy of a family (the so-called melonic family) of large-$N$ moments in arbitrary tensor models. This reduces the number of independent entries in the positive semidefinite matrices that build the core of the tensor bootstrap (for tensor models there are already several generalizations of the positive semidefinite Toeplitz and Hankel matrices of lattice gauge theory and random matrix bootstrap, respectively). More concretely, we prove that any melonic operator $C$ at large-$N$ has an expectation value that depends on $C$ exclusively through its degree. A similar statement is shown here to hold for the Schwinger-Dyson equations of melonic moments. The strength of our result is also its scope, which is not limited to melonic tensor models.