THETA-VACUA, CONFINEMENT AND THE CONTINUUM-LIMIT

We investigate the dependence of the CP3 model and of the SU(2) Yang-Mills theory on the vacuum angle theta. The CP3 model exhibits a first order deconfining phase transition in theta. The critical value of a runs from sr 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.