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