Holographic Krylov spread complexity for a confining multi-charge AdS soliton

We study holographic spread complexity for a Type IIB solution dual to a deformation of $\mathcal{N}=4$ SYM that flows to a confining (2+1)-dimensional supersymmetric theory in the IR. We use the proposal that relates the rate of change of spread complexity of local operators with the proper momentum of an infalling probe particle in the bulk. We analyse two cases: a probe particle falling radially and a probe falling radially while rotating with conserved angular momentum. We elaborate on how to define the proper coordinate in the presence of a conserved Noether charge using the Routhian. The trajectories for the probes were studied numerically, revealing an oscillatory behaviour of the complexity.