  We study the effect of dense quarks in a SU(N) matrix model of deconfinement.
For three or more colors, the quark contribution to the loop potential is
complex. After adding the charge conjugate loop, the measure of the matrix
integral is real, but not positive definite. In a matrix model, quarks act like
a background Z(N) field; at nonzero density, the background field also has an
imaginary part, proportional to the imaginary part of the loop. Consequently,
while the expectation values of the loop and its complex conjugate are both
real, they are not equal. These results suggest a possible approach to the
fermion sign problem in lattice QCD.
