  We investigate the dependence of the CP^3 model and of the SU(2) Yang-Mills
theory on the vacuum angle theta. The CP^3 model exhibits a first order
deconfining phase transition in theta. The critical value of theta runs from pi
in the strong coupling limit towards zero as beta is taken to infinity.
Qualitatively the same behavior is found in the SU(2) Yang-Mills theory in four
dimensions. We discuss the renormalization group trajectories. Only the line
with theta = 0 allows the cut-off to go to infinity, while the lines with theta
> 0 end on the line of first order phase transitions. Thus theta is forced to
zero in the continuum limit.
