Topological defects and confinement with machine learning: The case of monopoles in compact electrodynamics

M N Chernodub,V A Goy,Harold Erbin,A V Molochkov

doi:10.1103/physrevd.102.054501

Abstract

We investigate the advantages of machine learning techniques to recognize the dynamics of topological objects in quantum field theories. We consider the compact U(1) gauge theory in three spacetime dimensions as the simplest example of a theory that exhibits confinement and mass gap phenomena generated by monopoles. We train a neural network with a generated set of monopole configurations to distinguish between confinement and deconfinement phases, from which it is possible to determine the deconfinement transition point and to predict several observables. The model uses a supervised learning approach and treats the monopole configurations as three-dimensional images (holograms). We show that the model can determine the transition temperature with accuracy, which depends on the criteria implemented in the algorithm. More importantly, we train the neural network with configurations from a single lattice size before making predictions for configurations from other lattice sizes, from which a reliable estimation of the critical temperatures are obtained.

Highlights

Compact Abelian gauge model in two spatial dimensions mimics several exciting nonperturbative features of quantum chromodynamics (QCD), including the linear confinement of electric charges at large distances and mass-gap generation [1]
We provide a basic description of the compact electrodynamics on the lattice, the lattice monopoles, and the relevant observables in Sec
The aim of this section it to describe the results of how the neural network may learn the dynamics of monopoles and predict the various observables as well as the position of the deconfinement transition

Summary

Introduction

Compact Abelian gauge model in two spatial dimensions mimics several exciting nonperturbative features of quantum chromodynamics (QCD), including the linear confinement of electric charges at large distances and mass-gap generation [1]. This Abelian toy model—often called compact electrodynamics, or cQED—possesses topologically stable objects, monopoles, which reveal themselves as instantons. The chiral symmetry plays a very important role in the hadronic physics described by QCD. Both QCD and cQED experience a finite-temperature transition to a high-temperature phase that lacks the linear confinement property

Objectives

Results

Conclusion