Qcd Phases in Lattice Qcd

It is believed that QCD undergoes phase transitions as temperature T and the baryon density, controlled by a chemical potential μ, increase. For example, an expected phase structure is found in Fig.1 of ref. 1. To theoretically investigate what really happens at non-zero T and μ in QCD, lattice calculations seem ideal. Indeed, as reviewed in ref. 2, lattice QCD investigations are very successful at finite T but μ = 0. On the other hand, lattice QCD simulations at non-zero μ have remained to be extremely difficult for a long time, since a complex nature of the lattice QCD action in this case makes a direct application of straightforward Monte-Carlo methods impossible. Recently, however, several new techniques have been proposed to overcome this difficulty and some of them give promising results. In this talk I mainly review recent progresses in lattice QCD at non-zero μ.