Complex Saddle Points and Disorder Lines in QCD at finite temperature and density

Abstract

The properties and consequences of complex saddle points are explored in phenomenological models of QCD at non-zero temperature and density. Such saddle points are a consequence of the sign problem, and should be considered in both theoretical calculations and lattice simulations. Although saddle points in finite-density QCD are typically in the complex plane, they are constrained by a symmetry that simplifies analysis. We model the effective potential for Polyakov loops using two different potential terms for confinement effects, and consider three different cases for quarks: very heavy quarks, massless quarks without modeling of chiral symmetry breaking effects, and light quarks with both deconfinement and chiral symmetry restoration effects included in a pair of PNJL models. In all cases, we find that a single dominant complex saddle point is required for a consistent description of the model. This saddle point is generally not far from the real axis; the most easily noticed effect is a difference between the Polyakov loop expectation values $⟨{\mathrm{Tr}}_{F}P⟩$ and $⟨{\mathrm{Tr}}_F{P}^{†}⟩$, and that is confined to small region in the $\mu -T$ plane. In all but one case, a disorder line is found in the region of critical and/or crossover behavior. The disorder line marks the boundary between exponential decay and sinusoidally modulated exponential decay of correlation functions. Disorder line effects are potentially observable in both simulation and experiment. Precision simulations of QCD in the $\mu -T$ plane have the potential to clearly discriminate between different models of confinement.

33 pages, 20 figures

References in corpus (7)

• The Phase Structure of the Polyakov--Quark-Meson Model
• Center-stabilized Yang-Mills theory: confinement and large $N$ volume independence
• Abelian duality, confinement, and chiral symmetry breaking in QCD(adj)
• Stochastic quantization at finite chemical potential
• New Phases of SU(3) and SU(4) at Finite Temperature
• Complex Langevin dynamics and other approaches at finite chemical potential
• Baryon Number Correlations in Heavy Ion Collisions

Cited by in corpus (7)

• Evading the sign problem in the mean-field approximation through Lefschetz-thimble path integral
• One-dimensional QCD in thimble regularization
• Application of the path optimization method to the sign problem in an effective model of QCD with a repulsive vector-type interaction
• Strong-interaction matter under extreme conditions from chiral quark models with nonlocal separable interactions
• Perturbative aspects of the deconfinement transition -- Physics beyond the Faddeev-Popov model
• Complex spectrum of spin models for finite-density QCD
• Complex saddle points in finite-density QCD