Topology Change and theta-Vacua in 2D Yang-Mills Theory

Abstract

We discuss the existence of $θ$-vacua in pure Yang-Mills theory in two space-time dimensions. More precisely, a procedure is given which allows one to classify the distinct quantum theories possessing the same classical limit for an arbitrary connected gauge group G and compact space-time manifold M (possibly with boundary) possessing a special basepoint. For any such G and M it is shown that the above quantizations are in one-to-one correspondence with the irreducible unitary representations (IUR's) of $π_1(G)$ if M is orientable, and with the IUR's of $π_1(G)/2π_1(G)$ if M is nonorientable.