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Lattice Yang-Mills is a discrete probabilistic model of random matrices on a graph aiming at describing the quantum Yang-Mills theory in particle physics. Gauge/string duality is a principle that states that the observables of Yang-Mills theory can be described in terms of random surfaces. In this talk, I will present a general gauge/string duality for the gauge group U(N) based on the Weingarten calculus developed by Collins and Sniady, and recently refined by Magee-Puder, Dahlqvist, and myself, based on the Schur-Weyl duality for rational representations of U(N).