  The gradient flow in non-abelian gauge theories on R^4 is defined by a local
diffusion equation that evolves the gauge field as a function of the flow time
in a gauge-covariant manner. Similarly to the case of the Langevin equation,
the correlation functions of the time-dependent field can be expanded in
perturbation theory, the Feynman rules being those of a renormalizable field
theory on R^4 x [0,oo). For any matter multiplet and to all loop orders, we
show that the correlation functions are finite, i.e. do not require additional
renormalization, once the theory in four dimensions is renormalized in the
usual way. The flow thus maps the gauge field to a one-parameter family of
smooth renormalized fields.

High Energy Physics - Theory;High Energy Physics - Lattice