Duality of O(N) and Sp(N) random tensor models: tensors with symmetries

TL;DR

This paper extends the duality between orthogonal and symplectic random tensor models to include tensors with permutation symmetries, broadening the scope of previous duality results to symmetric and anti-symmetric tensors.

Contribution

It generalizes the duality to tensor models with permutation symmetries, including totally symmetric and anti-symmetric tensors, for interactions of arbitrary order.

Findings

Duality holds for symmetric and anti-symmetric tensors

Results apply to models with arbitrary interaction order

Extends previous duality results to more symmetric tensor models

Abstract

In a recent series of papers, a duality between orthogonal and symplectic random tensor models has been proven, first for quartic models and then for models with interactions of arbitrary order. However, the tensor models considered so far in the literature had no symmetry under permutation of the indices. In this paper, we generalize these results for tensors models with interactions of arbitrary order which further have non-trivial symmetry under the permutation of the indices. Totally symmetric and anti-symmetric tensors are thus treated as a particular case of our result.