Stochastic Renormalization Group and Gradient Flow

Understand

A non-perturbative and continuous definition of RG transformations as stochastic processes is proposed, inspired by the observation that the functional RG equations for effective Boltzmann factors may be interpreted as Fokker-Planck equations.

• The result implies a new approach to Monte Carlo RG that is amenable to lattice simulation.
• Long-distance correlations of the effective theory are shown to approach gradient-flowed correlations, which are simpler to measure.
• The Markov property of the stochastic RG transformation implies an RG scaling formula which allows for the measurement of anomalous dimensions when transcribed into gradient flow expectation values.