Perturbative analysis of the gradient flow in non-abelian gauge theories

Understand

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.