  The structure of S-duality in U(1) gauge theory on a 4-manifold M is examined
using the formalism of noncommutative geometry. A noncommutative space is
constructed from the algebra of Wilson-'t Hooft line operators which encodes
both the ordinary geometry of M and its infinite-dimensional loop space
geometry. S-duality is shown to act as an inner automorphism of the algebra and
arises as a consequence of the existence of two independent Dirac operators
associated with the spaces of self-dual and anti-selfdual 2-forms on M. The
relations with the noncommutative geometry of string theory and T-duality are
also discussed.
