S-duality in Abelian gauge theory revisited

Abstract

Definition of the partition function of U(1) gauge theory is extended to a class of four-manifolds containing all compact spaces and certain asymptotically locally flat (ALF) ones including the multi-Taub--NUT spaces. The partition function is calculated via zeta-function regularization with special attention to its modular properties. In the compact case, compared with the purely topological result of Witten, we find a non-trivial curvature correction to the modular weights of the partition function. But S-duality can be restored by adding gravitational counter terms to the Lagrangian in the usual way. In the ALF case however we encounter non-trivial difficulties stemming from original non-compact ALF phenomena. Fortunately our careful definition of the partition function makes it possible to circumnavigate them and conclude that the partition function has the same modular properties as in the compact case.

LaTeX; 22 pages, no figures

References in corpus (5)

• Moduli Spaces of Instantons on the Taub-NUT Space
• Gauge Theory and Langlands Duality
• The topology of asymptotically locally flat gravitational instantons
• Surface Operators in Abelian Gauge Theory
• Surface Operators in N=2 Abelian Gauge Theory

Cited by in corpus (5)

• Higher abelian gauge theory associated to gerbes on noncommutative deformed M5-branes and S-duality
• Abelian instantons over the Chen-Teo AF geometry
• Electric-magnetic Duality of Abelian Gauge Theory on the Four-torus, from the Fivebrane on T2 x T4, via their Partition Functions
• The four dimensional Yang--Mills partition function in the vicinity of the vacuum
• The Berry connection of the Ginzburg-Landau vortices