  The mixing between the chiral condensate and the density in hot and dense QCD
matter is familiar. We show that the mixing relevant for the ground state is
considerably more extensive, and in particular also involves gluonic degrees of
freedom. As a result, the Hessian of the QCD effective action is non-Hermitian,
but retains a symmetry under combined charge- and complex conjugation. This can
lead to complex-conjugate pairs of eigenvalues of this Hessian, signaling
regimes with spatially modulated correlations. Furthermore, based on the
analytic structure of the quark determinant at a chiral critical point, we
demonstrate that the corresponding massless critical mode is composed of the
chiral condensate, the density and the Polyakov loops. Due to an avoided
crossing, the critical mode turns out to be disconnected from the chiral
condensate in vacuum. We present general arguments for all these features and
illustrate them through explicit model calculations.
