Can θ/N dependence for gluodynamics be compatible with 2π periodicity in θ?: art. no. 054016

In a number of field theoretical models the vacuum angle a enters physics in the combination theta/N, where N stands generically for the number of colors or flavors, in an apparent contradiction with the expected 2 pi periodicity in theta. We argue that a resolution of this puzzle is related to the existence of a number of different theta dependent sectors in a finite volume formulation, which cannot be seen in the naive thermodynamic limit V-->infinity. It is shown that, when the limit V-->infinity is properly defined, physics is always 2 pi periodic in theta for any integer, and even rational, values of N, with vacuum doubling at certain values of theta. We demonstrate this phenomenon in both the multiflavor Schwinger model with the bosonization technique, and four-dimensional gluodynamics with the effective Lagrangian method. The proposed mechanism works for an arbitrary gauge group. [S0556-2821(98)01717-2]