Stochastic Renormalization Group and Gradient Flow

Abstract

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.

arXiv comment18 pages

References in corpus (11)

• The Exact Renormalisation Group and Approximate Solutions
• Trivializing maps, the Wilson flow and the HMC algorithm
• Infinite N phase transitions in continuum Wilson loop operators
• Fundamentals of the Exact Renormalization Group
• A Monte Carlo study of leading order scaling corrections of phi^4 theory on a three dimensional lattice
• Nonperturbative Renormalization of Operators in Near-Conformal Systems Using Gradient Flows
• Gradient flow and the renormalization group
• Derivation of a Gradient Flow from ERG
• Gradient flow and the Wilsonian renormalization group flow
• The Yang-Mills gradient flow and lattice effective action
• The exact renormalization group in Astrophysics

Cited by in corpus (9)

• Gradient flow exact renormalization group
• Hadronic vacuum polarization using gradient flow
• $\Lambda$ parameter of the SU(3) Yang-Mills theory from the continuous $\beta$ function
• Gradient flow exact renormalization group -- inclusion of fermion fields
• Fixed Point Structure of Gradient Flow Exact Renormalization Group for Scalar Field Theories
• Chiral anomaly as a composite operator in the gradient flow exact renormalization group formalism
• A basis of the gradient flow exact renormalization group for gauge theory
• Simulating Nelsonian Quantum Field Theory
• Journey from the Wilson exact RG towards the Wegner-Morris Fokker-Planck RG and the Carosso field-coarsening via Langevin stochastic processes