U(1) gauge theory onR 4 is known to possess an electric-magnetic duality symmetry that inverts the coupling constant and extends to an action ofSL(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 whenN=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 b 2 + ≤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.
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Witten, E. OnS-duality in Abelian gauge theory. Selecta Mathematica, New Series 1, 383–410 (1995). https://doi.org/10.1007/BF01671570
- Gauge Theory
- Partition Function
- Essential Role
- Modular Form
- Abelian Gauge