Orthogonal bases of invariants in tensor models

Abstract

Representation theory provides an efficient framework to count and classify invariants in tensor models of (gauge) symmetry G_d = U(N₁) ⊗ · · · ⊗ U(N_d) . We show that there are two natural ways of counting invariants, one for arbitrary G_d and another valid for large rank of G_d. We construct basis of invariant operators based on the counting, and compute correlators of their elements. The basis associated with finite rank of G_d diagonalizes two-point function. It is analogous to the restricted Schur basis used in matrix models. We comment on future directions for investigation.