Dirac spectrum in complex Langevin simulations of QCD

We show that the spectrum of the Dirac operator in complex Langevin simulations of QCD at nonzero chemical potential must behave in a way which is radically different from the one in simulations with ordinary noncomplexified gauge fields: at low temperatures the small eigenvalues of the Dirac operator must be inside the quark mass for chemical potentials as large as a third of the nucleon mass. In particular, in the chiral limit the Dirac eigenvalues of complex Langevin simulations must accumulate at the origin.