The chiral limit in lattice QCD

It has been a big challenge for lattice QCD to simulate dynamical quarks near the chiral limit. Theoretically, it is well-known that the naive chiral symmetry cannot be realized on the lattice (the Nielsen-Ninomiya theorem). Also practically, the computational cost rapidly grows as the quark mass is reduced. The JLQCD collaboration started a project to perform simulations with exact but modified chiral symmetry using the the overlap-Dirac operator and the topology conserving action. The latter is helpful to reduce the numerical cost of the dynamical quarks. Our simulation of two-flavor QCD has been successful to reduce the sea quark mass down to a few MeV.Comment: Talk given at SCGT 06, (minor changes and the references added.