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Random tensor models for a generic complex tensor generalize matrix models inarbitrary dimensions and yield a theory of random geometries. They support a1/N expansion dominated by graphs of spherical topology. Their Schwinger Dysonequations, generalizing the loop equations of matrix models, translate intoconstraints satisfied by the partition function. The constraints have beenshown, in the large N limit, to close a Lie algebra indexed by colored rootedD-ary trees yielding a first generalization of the Virasoro algebra inarbitrary dimensions. In this paper we complete the Schwinger Dyson equationsand the associated algebra at all orders in 1/N. The full algebra ofconstraints is indexed by D-colored graphs, and the leading order D-ary treealgebra is a Lie subalgebra of the full constraints algebra.

The Schwinger Dyson equations and the algebra of constraints of random tensor models at all orders