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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 iscomplex. After adding the charge conjugate loop, the measure of the matrixintegral is real, but not positive definite. In a matrix model, quarks act likea background Z(N) field; at nonzero density, the background field also has animaginary part, proportional to the imaginary part of the loop. Consequently,while the expectation values of the loop and its complex conjugate are bothreal, they are not equal. These results suggest a possible approach to thefermion sign problem in lattice QCD.Comment: 9 pages, 3 figure

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

Dense quarks, and the fermion sign problem, in a<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>S</mml:mi><mml:mi>U</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>N</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>matrix model

Dense quarks, and the fermion sign problem, in aSU(N)matrix model