  The time-dependent scaling of the two-time autocorrelation function of spin
systems without disorder undergoing phase-ordering kinetics is considered. Its
form is shown to be determined by an extension of dynamical scaling to a local
scale-invariance which turns out to be a new version of conformal invariance.
The predicted autocorrelator is in agreement with Monte-Carlo data on the
autocorrelation function of the 2D kinetic Ising model with Glauber dynamics
quenched to a temperature below criticality.
