Lecture Notes on Normalizing Flows for Lattice Quantum Field Theories

Abstract

Numerical simulations of quantum field theories on lattices serve as a fundamental tool for studying the non-perturbative regime of the theories, where analytic tools often fall short. Challenges arise when one takes the continuum limit or as the system approaches a critical point, especially in the presence of non-trivial topological structures in the theory. Rapid recent advances in machine learning provide a promising avenue for progress in this area. These lecture notes aim to give a brief account of lattice field theories, normalizing flows, and how the latter can be applied to study the former. The notes are based on the lectures given by the first author in various recent research schools.