  We study the behavior of the fermion determinant at finite temperature and
chemical potential, as a function of the Polyakov loop. The phase of the
determinant is correlated with the imaginary part of the Polyakov loop. This
correlation and its consequences are considered in static QCD, in a toy model
of free quarks in a constant $A_0$ background, and in simulations constraining
the imaginary part of the Polyakov loop to zero.
