# Orthogonal Bases of Invariants in Tensor Models

## TL;DR

This paper develops two methods for counting and constructing invariant operators in tensor models, providing bases that simplify correlator computations and extend concepts from matrix models to higher-rank tensors.

## Contribution

It introduces two natural counting approaches for invariants in tensor models and constructs bases that diagonalize correlators, extending matrix model techniques.

## Key findings

- Finite N basis diagonalizes two-point functions
- Large N counting method applicable for asymptotic analysis
- Constructed invariant bases analogous to restricted Schur basis

## 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.