### Renormalization Group Flow as Optimal Transport

Semon Rezchikov, Harvard University*Abstract:*

In this talk, I will describe how the renormalization group (RG), a fundamental aspect of statistical in quantum field theory, can be cast as a variational problem using ideas from optimal transport. I will review the renormalization group as well as optimal transport for non-specialists. The latter subject is naturally connected to methods in machine learning. This variational formulation of RG, beyond having theoretical interest, can be used to design neural networks which compute the renormalization group flow of conventional field theories. The renormalization group has been fundamental in the design of the numerical algorithms for finding ground states and computing physical quantities of 1+1 dimensional field theories which have been successful thus far. I will discuss the prospects for using this formulation of RG to merge modern techniques from machine learning with ideas involving renormalization, in order to tackle fundamental problems in the study in field theories of dimension greater than 1+1.