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We study the relation between the continuum threshold as function of thetemperature $s_0(T)$ within finite energy sum rules and the trace of thePolyakov loop $\Phi$ in the framework of a nonlocal SU(2) chiral quark model,establishing a contact between both deconfinement order parameters at finitetemperature $T$ and chemical potential $\mu$. In our analysis, we also includethe order parameter for the chiral symmetry restoration, the chiral quarkcondensate.  We found that $s_0$ and $\Phi$ providing us the same information for thedeconfinement transition, both for the zero and finite chemical potentialcases. At zero density, the critical temperatures for both quantities coincideexactly and, at finite $\mu$ both order parameters provide evidence for theappearance of a quarkyonic phase.

Comparison between the continuum threshold and the Polyakov loop as deconfinement order parameters