TY - JOUR

T1 - Supersymmetric Yang-Mills theory and integrable systems

AU - Donagi, Ron

AU - Witten, Edward

N1 - Funding Information:
I Research supported in part by NSF grant DMS95-03249 and Unite mixte de service de I'institut H. PoincarE, CNRS - UniversitE Pien'e et Marie Curie, Paris. 2 Research supported in part by NSF grant PHY92-453.

PY - 1996/2/5

Y1 - 1996/2/5

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0030569824&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030569824&partnerID=8YFLogxK

U2 - 10.1016/0550-3213(95)00609-5

DO - 10.1016/0550-3213(95)00609-5

M3 - Article

AN - SCOPUS:0030569824

VL - 460

SP - 299

EP - 334

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

IS - 2

ER -