Exact renormalization groups and transportation of measures

Abstract

This note provides a new perspective on Polchinski's exact renormalization group, by explaining how it gives rise, via the multiscale Bakry-Émery criterion, to Lipschitz transport maps between Gaussian free fields and interacting quantum and statistical field theories. Consequently, many functional inequalities can be verified for the latter field theories, going beyond the current known results.

Mathematical typos fixed in Main Theorem and functional inequalities results