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On S-Duality in Abelian Gauge Theory

High Energy Physics - Theory 2010-04-07 v1 alg-geom Algebraic Geometry

Abstract

U(1) gauge theory on R4{\bf R}^4 is known to possess an electric-magnetic duality symmetry that inverts the coupling constant and extends to an action of SL(2,Z)SL(2,{\bf 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+1b_2^+\leq 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.

Keywords

Cite

@article{arxiv.hep-th/9505186,
  title  = {On S-Duality in Abelian Gauge Theory},
  author = {Edward Witten},
  journal= {arXiv preprint arXiv:hep-th/9505186},
  year   = {2010}
}

Comments

32 pages, harvmac