Prospects for perfect actions

Abstract

The fixed-point (FP) action in QCD, although it is local and determined by classical equations, is difficult to parametrize well and is expensive to simulate. But the stake is high: the FP action has scale invariant instanton solutions, has no topological artifacts, satisfies the index theorem on the lattice, does not allow exceptional configurations, requires no tuning to get the pion massless and is expected to reduce the cut-off effects significantly. An overview is given including a discussion on tests in Yang-Mills theory, QCD and $d=2$ spin and gauge models.