Simulating QCD at finite density

Abstract

In this review, I recall the nature and the inevitability of the "sign problem" which plagues attempts to simulate lattice QCD at finite baryon density. I present the main approaches used to circumvent the sign problem at small chemical potential. I sketch how one can predict analytically the severity of the sign problem, as well as the numerically accessible range of baryon densities. I review progress towards the determination of the pseudo-critical temperature T_c(mu), and towards the identification of a possible QCD critical point. Some promising advances with non-standard approaches are reviewed.

Comments: 23 pages, Plenary talk at the 27th International Symposium on Lattice Field Theory (Lattice 2009), Beijing, China, 25-31 July 2009; v2: two small corrections in the complex Langevin section