Supersymmetric Yang-Mills theory and integrable systems

Ron Donagi, Edward Witten

Research output: Contribution to journalArticlepeer-review

539 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)299-334
Number of pages36
JournalNuclear Physics B
Issue number2
StatePublished - Feb 5 1996
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics


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