Abstract
We study the localization properties of the low-lying Dirac eigenmodes in QCD at imaginary chemical potential $\hat{\mu}_I=\pi$ at temperatures above the Roberge-Weiss transition temperature $T_{\rm RW}$. We find that modes are localized up to a temperature-dependent "mobility edge" and delocalized above it, and that the mobility edge extrapolates to zero at a temperature compatible with $T_{\rm RW}$. This supports the existence of a strong connection between localization of the low Dirac modes and deconfinement, studied here for the first time in a model with a genuine deconfinement transition in the continuum limit in the presence of dynamical fermions.
Highlights
The interest in gauge theories at nonzero imaginary chemical potential is due both to practical and theoretical reasons
The analog of center symmetry in the case of SUðNcÞ theories with dynamical fundamental fermions is the Roberge-Weiss (RW) symmetry [18] that states that the partition function is periodic in the reduced imaginary chemical potential μ I 1⁄4 μI=T with period 2π=Nc
We studied Nf 1⁄4 2 þ 1 QCD on N3s × Nt hypercubic lattices using two-stout improved [80] rooted staggered fermions with physical quark masses, at finite temperature T 1⁄4 1=ðaNtÞ and in the presence of an imaginary chemical potential μI
Summary
The interest in gauge theories at nonzero imaginary chemical potential is due both to practical and theoretical reasons. Localization in the presence of a sharp transition has been mostly investigated in pure gauge theories, selecting the “physical” center sector (i.e., real positive expectation value of the Polyakov loop) in the spontaneously broken phase In these cases, localization and deconfinement have been shown to coincide within numerical uncertainties [64,65,66,67,68]. For gauge group SUð3Þ and μ I 1⁄4 π, these correspond to the two complex sectors eÆi23π, which leaves an exact Z2 center symmetry that can break down spontaneously This happens at TRW, where the system undergoes a second order phase transition to a deconfined phase, where either of the two complex sectors can be selected, and the local Polyakov loops prefer to align to either ei23π or e−i23π.
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