N = 4 $\mathcal{N}=4$ supersymmetric Yang-Mills theories with algebra so ( ) $\mathfrak {so}(4N)$ and appropriate choices of global structure can have non-invertible symmetries. We identify the branes holographically dual to symmetries, derive fusion rules for symmetries from worldvolume dynamics on branes.

In this article, only connected bipartite graphs G with a unique perfect matching M are considered. Let Gw denote the weighted graph obtained from G by giving weights to its edges using the positive weight function w : E(G)→ (0,∞) such that w(e) = 1 for each e ∈ M. An unweighted graph G may be viewed as a weighted graph with the weight function w ≡ 1 (all ones vector). A weighted graph Gw is no...