On S-duality in Abelian gauge theory

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U(1) gauge theory on R4 is known to possess an electric-magnetic duality symmetry that inverts the coupling constant and extends to an action of SL(2, Z). In this paper, the duality is studied on a general four-manifold and it is shown that the partition function is not a modular-invariant function but transforms as a modular form. This result plays an essential role in determining a new low-energy interaction that arises when N=2 supersymmetric Yang-Mills theory is formulated on a four-manifold; the determination of this interaction gives a new test of the solution of the model and would enter in computations of the Donaldson invariants of four-manifolds with b2+≤1. Certain other aspects of abelian duality, relevant to matters such as the dependence of Donaldson invariants on the second Stieffel-Whitney class, are also analyzed.

Original languageEnglish (US)
Pages (from-to)383-410
Number of pages28
JournalSelecta Mathematica, New Series
Issue number2
StatePublished - Sep 1995
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • General Physics and Astronomy


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