Approaches to the sign problem in lattice field theory

TL;DR

This paper reviews the sign problem in lattice field theories, focusing on recent methods like dualization to world-line representations and the density-of-states approach to address complex actions in finite-density quantum field theories.

Contribution

It provides a comprehensive review of the sign problem and introduces recent strategies such as dualization and density-of-states methods for tackling complex actions.

Findings

Dualization to world-line representations offers a promising way to mitigate the sign problem.

Density-of-states approach provides an alternative framework for complex action simulations.

The review highlights the strengths and limitations of recent methods in addressing the sign problem.

Abstract

Quantum field theories (QFTs) at finite densities of matter generically involve complex actions. Standard Monte-Carlo simulations based upon importance sampling, which have been producing quantitative first principle results in particle physics for almost fourty years, cannot be applied in this case. Various strategies to overcome this so-called Sign Problem or Complex Action Problem were proposed during the last thirty years. We here review the sign problem in lattice field theories, focussing on two more recent methods: Dualization to world-line type of representations and the density-of-states approach.