The sign problem in the $\epsilon$-regime of QCD

Abstract

QCD in the $\epsilon$-regime at nonzero baryon chemical potential $\mu$ is reviewed. The focus is on aspects of the sign problem which are relevant for lattice QCD. It is discussed how spontaneous chiral symmetry breaking and the sign problem are related through the spectrum of the Dirac operator. The strength of the sign problem is linked to the quark mass and the chemical potential. Specific implications for lattice QCD are discussed.