Electric-magnetic Duality in Noncommutative Geometry

Details Electric-magnetic Duality in Noncommutative Geometry Electric-magnetic Duality in Noncommutative Geometry

1997-09-28

arxiv.org/abs/hep-th/9709198v1

Phys.Lett. B417 (1998) 303-311

Physics

High Energy Physics

High Energy Physics - Theory

13 pages LaTeX, no figures

Scientific paper

10.1016/S0370-2693(97)01401-9

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.

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