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

TL;DR

This paper investigates large-N QCD with nonzero chemical potential using spacetime reduction, proposing a method to mitigate sign problems, and confirms its effectiveness through numerical tests and analysis of physical observables.

Contribution

It introduces a re-summation technique to suppress sign fluctuations in reduced large-N QCD at finite density, validated by numerical experiments in two dimensions.

Findings

Successfully solves the silver-blaze problem in 2D QCD.

Shows independence of free energy and chiral condensate from chemical potential in the hadronic phase.

Finds the phase distribution aligns with chiral perturbation theory predictions.

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 theta of its Dirac determinant, and its chiral condensate <psi-bar-psi>. We show that F and <psi-bar-psi> are independent of mu in the hadronic phase but that, as chiral perturbation theory predicts, the quenched chiral condensate drops from its mu=0 value when mu~(pion mass)/2. Finally, we find that the distribution of theta qualitatively agrees with further, more recent, predictions from chiral perturbation theory.