Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
1997-11-20
Phys.Rev. D58 (1998) 054016
Physics
High Energy Physics
High Energy Physics - Phenomenology
minor changes in the discussion, a few references are added
Scientific paper
10.1103/PhysRevD.58.054016
In a number of field theoretical models the vacuum angle \theta 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 can not be seen in the naive thermodynamic limit V -> \infty. It is shown that, when the limit V -> \infty 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 multi-flavor Schwinger model with the bosonization technique, and four-dimensional gluodynamics with the effective Lagrangian method. The proposed mechanism works for an arbitrary gauge group.
Halperin Igor
Zhitnitsky Ariel
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