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

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

1996-12-29

arxiv.org/abs/hep-th/9612246v1

Nucl.Phys. B500 (1997) 565-578

Physics

High Energy Physics

High Energy Physics - Theory

16 pages, 4 figures, uses harvmac and psbox

Scientific paper

10.1016/S0550-3213(97)00378-7

We discuss the existence of $\theta$-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 $\pi_1(G)$ if M is orientable, and with the IUR's of $\pi_1(G)/2\pi_1(G)$ if M is nonorientable.

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