Abstract
The Coulomb branch of N = 2 supersymmetric gauge theories in four dimensions is described in general by an integrable Hamiltonian system in the holomorphic sense. A natural construction of such systems comes from two-dimensional gauge theory and spectral curves. Starting from this point of view, we propose an integrable system relevant to the N = 2 SU( n) gauge theory with a hypermultiplet in the adjoint representation, and offer much evidence that it is correct. The model has an SL(2, Z) S-duality group (with the central element −1 of SL(2, Z) acting as charge conjugation); SL(2, Z) permutes the Higgs, confining, and oblique confining phases in the expected fashion. We also study more exotic phases.
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