The vacuum theta-angle is zero in non-abelian gauge theories

Abstract

We argue that gauge transformations with arbitrary fractional winding numbers should be allowed in a non-Abelian gauge theory. This eliminates the topological distinction between large and small gauge transformations. We prove that the states which satisfy the Gauss's law constraint are strictly invariant under gauge transformations, i.e. no phase shift occurs. In other words, the vacuum θ-angle is zero. Our observation does not resolve the strong CP problem.