Gradient flow and the renormalization group

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We investigate the renormalization group (RG) structure of the gradient flow.

• Instead of using the original bare action to generate the flow, we propose to use the effective action at each flow time.
• We write down the basic equation for scalar field theory that determines the evolution of the action, and argue that the equation can be regarded as a RG equation if one makes a field-variable transformation at every step such that the kinetic term is kept to take the canonical form.
• We consider a local potential approximation (LPA) to our equation, and show that the result has a natural interpretation with Feynman diagrams.