Supersymmetric Yang-Mills Systems And Integrable Systems

Details Supersymmetric Yang-Mills Systems And Integrable Systems Supersymmetric Yang-Mills Systems And Integrable Systems

1995-10-16

arxiv.org/abs/hep-th/9510101v2

Nucl.Phys.B460:299-334,1996

Physics

High Energy Physics

High Energy Physics - Theory

50 pages, harvmac. added references

Scientific paper

10.1016/0550-3213(95)00609-5

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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