Duality of orthogonal and symplectic random tensor models

Abstract

The groups $\mathrm{O}(N)$ and $\mathrm{Sp}(N)$ are related by an analytic continuation to negative values of $N$, $\mathrm{O}(-N)\simeq \mathrm{Sp}(N)$. This duality has been studied for vector models, $\mathrm{SO}(N)$ and $\mathrm{Sp}(N)$ 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.