Orthogonal Bases of Invariants in Tensor Models

Abstract

Representation theory provides a suitable framework to count and classify invariants in tensor models. We show that there are two natural ways of counting invariants, one for arbitrary rank of the gauge group and a second, which is only valid for large N. We construct bases of invariant operators based on the counting, and compute correlators of their elements. The basis associated with finite N diagonalizes the two-point function of the theory and it is analogous to the restricted Schur basis used in matrix models. We comment on future lines of investigation.

Two overlapping but independent results are merged to a joint work. 16 pages, 1 table

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• Matrix and tensor witnesses of hidden symmetry algebras
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• Backgrounds from Tensor Models: A Proposal
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