Large-N spacetime reduction and the sign and silver-blaze problems of dense QCD

Abstract

We study the spacetime-reduced (Eguchi-Kawai) version of large-N QCD with nonzero chemical potential. We explore a method to suppress the sign fluctuations of the Dirac determinant in the hadronic phase; the method employs a re-summation of gauge configurations that are related to each other by center transformations. We numerically test this method in two dimensions, and find that it successfully solves the silver-blaze problem. We analyze the system further, and measure its free energy F, the average phase θ of its Dirac determinant, and its chiral condensate $\left\langle {\bar{\psi }\psi } \right\rangle$. We show that F and $\left\langle {\bar{\psi }\psi } \right\rangle$ are independent of μ in the hadronic phase but that, as chiral perturbation theory predicts, the quenched chiral condensate drops from its μ = 0 value when μ ∼ (pion mass)/2. Finally, we find that the distribution of θ qualitatively agrees with further, more recent, predictions from chiral perturbation theory.