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arXiv · hep-th/9510101

Supersymmetric Yang-Mills Systems And Integrable Systems

Ron Donagi·Edward Witten
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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 $SL(2,{\bf Z})$ $S$-duality group (with the central element $-1$ of $SL(2,{\bf Z})$ acting as charge conjugation); $SL(2,{\bf Z})$ permutes the Higgs, confining, and oblique confining phases in the expected fashion. We also study more exotic phases.

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Ron Donagi, Edward Witten. 1995-10-23. Supersymmetric Yang-Mills Systems And Integrable Systems. https://doi.org/10.1016/0550-3213(95)00609-5

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