Triage of the Sign Problem

TL;DR

This paper investigates the sign problem in QCD at nonzero chemical potential, revealing that the traditional Banks-Casher formula does not hold and proposing an alternative mechanism based on chiral random matrix theory.

Contribution

It introduces a new understanding of the sign problem in QCD, showing the limitations of the Banks-Casher formula and providing an alternative spectral mechanism.

Findings

Banks-Casher formula is invalid for theories with a sign problem

An alternative spectral mechanism is proposed for QCD in one dimension

Chiral random matrix theory is used to analyze the sign problem

Abstract

We discuss the sign problem in QCD at nonzero chemical potential and its relation with chiral symmetry breaking and the spectrum of the Dirac operator using the framework of chiral random matrix theory. We show that the Banks-Casher formula is not valid for theories with a sign problem and has to be replaced by an alternative mechanism that is worked out in detail for QCD in one dimension at nonzero chemical potential.