Fixed point actions for SU(3) gauge theory

We summarize our recent work on the construction and properties of fixed point (FP) actions for lattice SU(3) pure gauge theory. These actions have scale invariant instanton solutions and their spectrum is exact through 1-loop, i.e. in their physical predictions there are no an nor g2an cut-off effects for any n. We present a few-parameter approximation to a classical FP action which is valid for short correlation lengths. We perform a scaling test of the action by computing the quantity G=Lσ(L), where the string tension σ(L) is measured from the torelon mass μ = Lσ(L), on lattices of fixed physical volume and varying lattice spacing a. While the Wilson action shows scaling violations of about ten per cent, the approximate fixed point action scales within the statistical errors for 12 ≥ aTc.