Vacuum Nodes in QCD at {ital {theta}}{bold =}{ital {bold {pi}}}: Exact Results

We show that the vacuum functional of 3+1 dimensional non abelian gauge theories vanishes for some classical field configurations {psi}{sub 0}({ital A})=0 when the coefficient of the CP violating {theta} term becomes {theta}={pi} (mod.2{pi}). Some of these classical configurations are explicitly identified and include sphalerons. The results shed new light into the nonperturbative behavior of nonabelian gauge theories and suggest a relevant role for these classical configurations in the confinement mechanism at {theta}=0. {copyright} {ital 1996 The American Physical Society.}