Abstract:

Asymptotically locally Euclidean (ALE) spaces arise in several areas of mathematical physics. Although locally Euclidean at infinity, they possess nontrivial topology in both their interior and asymptotic boundary, giving rise to phenomena absent on closed manifolds and on R^4. In this talk, I will review the topological features of ALE spaces that are most relevant to quantum field theory and address how the path integral on such noncompact backgrounds should be defined and interpreted. I will first examine Maxwell theory and show how S-duality provides a useful framework for organizing its boundary sectors and understanding the corresponding path integral. I will then discuss obstructions (anomalies) sensitive to the topology and asymptotic data of ALE spaces, and illustrate their implications for super-Yang--Mills theory and the Standard Model.