Abstract:
Since present Monte Carlo algorithms for lattice QCD may
become trapped in a fixed topological charge sector, it is
important to understand the effect of calculating at fixed
topology. In this work, we show that although the
restriction to a fixed topological sector becomes irrelevant
in the infinite volume limit, it gives rise to
characteristic finite size effects due to contributions from
all $\theta$-vacua. We calculate these effects and show how
to extract physical results from numerical data obtained at
fixed topology.