Duality of Orthogonal and Symplectic Random Tensor Models

Abstract

The groups $O(N)$ and $Sp(N)$ are related by an analytic continuation to negative values of $N$, $O(-N)\simeq Sp(N)$. This duality has been studied for vector models, $SO(N)$ and $Sp(N)$ gauge theories, as well as some random matrix ensembles. We extend this duality to real random tensor models of arbitrary order $D$ with no symmetry under permutation of the indices and with quartic interactions. The $N$ to $-N$ duality is shown to hold graph by graph to all orders in perturbation theory for the partition function, the free energy and the connected two point function.