Introductory lectures on lattice QCD at nonzero baryon number

TL;DR

This paper provides an accessible introduction to lattice QCD at nonzero baryon chemical potential, covering theoretical challenges, computational methods, and recent approaches for studying QCD under extreme conditions.

Contribution

It offers a comprehensive overview of methods and problems in lattice QCD at finite density, including sign problem solutions and complex Langevin dynamics, tailored for postgraduate students.

Findings

Discussion of the sign, overlap, and Silver Blaze problems

Overview of complex Langevin dynamics for finite density QCD

Summary of approaches to the phase boundary at small chemical potential

Abstract

These lecture notes contain an elementary introduction to lattice QCD at nonzero chemical potential. Topics discussed include chemical potential in the continuum and on the lattice; the sign, overlap and Silver Blaze problems; the phase boundary at small chemical potential; imaginary chemical potential; and complex Langevin dynamics. An incomplete overview of other approaches is presented as well. These lectures are meant for postgraduate students and postdocs with an interest in extreme QCD. A basic knowledge of lattice QCD is assumed but not essential. Some exercises are included at the end.