On subregion holographic complexity and renormalization group flows

We investigate subregion holographic complexity in the context of renormalization group flow geometries. We use both the Poinca\'re slicing and the Janus ansatz as holographic duals to renormalization group flows in the boundary conformal field theory. In the former metric, subregion complexity is computed for a disc and a strip shaped entangling region. For the disc shaped region, consistent emergence of length scales for flow to the deep infra-red is established. For strip shaped regions, we find that complexity cannot locate holographic phase transitions in a sharp domain wall scenario. For smooth domain walls, we find that the complexity might be an indicator of such phase transitions, and give numerical evidence that its derivative changes sign across a transition. Finally, the complexity is computed numerically using the Janus ansatz.