Poincaré symmetries and the yang-mills gradient flow

The latest developments have shown how to use the gradient flow (or Wilson flow, on the lattice) for the exploration of symmetries, and the definition of the corresponding renormalized Noether currents. In particular infinitesimal translations can be introduced along the gradient flow for gauge theories, and the corresponding Ward identities can be derived. When applied to lattice gauge theories, this approach leads to a possible strategy to renormalize the energy-momentum tensor nonperturbatively, and to study dilatations and scale invariance.