Singular Phases of Seiberg-Witten Integrable Systems: Weak and Strong Coupling

Details Singular Phases of Seiberg-Witten Integrable Systems: Weak and Strong Coupling Singular Phases of Seiberg-Witten Integrable Systems: Weak and Strong Coupling

2000-09-08

arxiv.org/abs/hep-th/0009060v2

Nucl.Phys. B595 (2001) 417-466

Physics

High Energy Physics

High Energy Physics - Theory

34 Pages, LaTeX, some typos and reference added

Scientific paper

10.1016/S0550-3213(00)00683-0

We consider the singular phases of the smooth finite-gap integrable systems arising in the context of Seiberg-Witten theory. These degenerate limits correspond to the weak and strong coupling regimes of SUSY gauge theories. The spectral curves in such limits acquire simpler forms: in most cases they become rational, and the corresponding expressions for coupling constants and superpotentials can be computed explicitly. We verify that in accordance with the computations from quantum field theory, the weak-coupling limit gives rise to precisely the "trigonometric" family of Calogero-Moser and open Toda models, while the strong-coupling limit corresponds to the solitonic degenerations of the finite-gap solutions. The formulae arising provide some new insights into the corresponding phenomena in SUSY gauge theories. Some open conjectures have been proven.

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