S-duality in N=2 supersymmetric gauge theories

A solution to the infinite coupling problem for N = 2 conformal supersymmetric gauge theories in four dimensions is presented. The infinitely-coupled theories are argued to be interacting superconformal field theories (SCFTs) with weakly gauged flavor groups. Consistency checks of this proposal are found by examining some low-rank examples. As part of these checks, we show how to compute new exact quantities in these SCFTs: the central charges of their flavor current algebras. Also, the isolated rank 1 E6 and E7 SCFTs are found as limits of Lagrangian field theories. 1. Infinite coupling and S-duality In many N = 2 supersymmetric gauge theories in four dimensions, an exactly marginal gauge coupling, g, can be taken infinite. In this paper we propose a new kind of quantum equivalence of gauge theories which relates such infinitely-strongly coupled theories to ones with both weakly-coupled (g ≪ 1) and strongly-coupled (g ∼ 1) sectors, but no infinitelystrongly coupled sectors. This proposal thus allows one to eliminate infinitely-coupled gauge theories in favor of merely strongly-coupled ones. In particular, it suggests that even as g → ∞ all the correlation functions of the theory remain finite! Our proposal generalizes the well-known S-duality of N = 4 supersymmetric gauge theories to the larger class of N = 2 supersymmetric ones. S-duality, or Olive-Montonen duality [1], inN = Im