Topology change and θ-vacua in 2D Yang-Mills theory Original Research Article

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 (IURʹs) of π1(G) if M is orientable, and with the IURʹs of π1(G)/2π1(G) if M is non-orientable.