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Abstract We compute the one-loop running of the SU(N) ’t Hooft coupof twelve-flavor SU(3) gauge theoryling in a finite volume gradient flow scheme using twisted boundary conditions. The coupling is defined in terms of the energy density of the gradient flow fields at a scale l ˜ $$ \tilde{l} $$ given by an adequate combination of the torus size and the rank of the gauge group, and is computed...