Relating lattice QCD and chiral perturbation theory

We present simulation results for quenched lattice QCD using chiral lattice fermions, which obey the Ginsparg-Wilson relation. In particular, we evaluated the low lying modes in Dirac spectrum and compared the results with the predictions based on Random Matrix Theory. The observed distributions agree well with the conjectured predictions in different topological sectors, if the physical volume exceeds about (1.2 fm)4. In this way we obtain direct information about the scalar condensate Sigma. We also measured the axial correlation functions for very light quarks in the ε-regime. Here the results can be compared with the predictions from quenched chiral perturbation theory. We observed a conclusive agreement in the sectors of topological charge 1 and 2, again with a similar lower bound for the volume. The matching of these correlation functions fixes a value for the pion decay constant Fπ. We have therefore obtained information on the two leading low energy constants of chiral perturbation theory, Sigma and Fπ, by simulating QCD as the underlying fundamental system. (author)