@article{71f4de91b2d84afb89840068620ef535,
title = "Renormalization group flow as optimal transport",
abstract = "We establish that Polchinski's equation for exact renormalization group (RG) flow is equivalent to the optimal transport gradient flow of a field-theoretic relative entropy. This provides a compelling information-theoretic formulation of the exact renormalization group, expressed in the language of optimal transport. A striking consequence is that a regularization of the relative entropy is in fact an RG monotone. We compute this monotone in several examples. Our results apply more broadly to other exact renormalization group flow equations, including widely used specializations of Wegner-Morris flow. Moreover, our optimal transport framework for RG allows us to reformulate RG flow as a variational problem. This enables new numerical techniques and establishes a systematic connection between neural network methods and RG flows of conventional field theories.",
author = "Jordan Cotler and Semon Rezchikov",
note = "Funding Information: We thank Kristan Jensen, Igor Klebanov, Nima Lashkari, Tim Morris, Yair Shenfeld, and Andrew Strominger for valuable discussions. We give a special thanks to Arthur Kosmala for identifying and correcting an error in our definition of the Wasserstein distance in the quantum field theory setting. J. C. is supported by a Junior Fellowship from the Harvard Society of Fellows, the Black Hole Initiative, as well as in part by the Department of Energy under Grant No. DE-SC0007870. S. R. is supported by the Simons Foundation Collaboration grant “Homological Mirror Symmetry and Applications” (Grant No. 385573). Publisher Copyright: {\textcopyright} 2023 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the {"}https://creativecommons.org/licenses/by/4.0/{"}Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by SCOAP3.",
year = "2023",
month = jul,
day = "15",
doi = "10.1103/PhysRevD.108.025003",
language = "English (US)",
volume = "108",
journal = "Physical Review D",
issn = "2470-0010",
publisher = "American Physical Society",
number = "2",
}