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

TL;DR

This paper analyzes the singular phases of Seiberg-Witten integrable systems, revealing how weak and strong coupling limits simplify spectral curves and connect to known integrable models, providing new insights into SUSY gauge theories.

Contribution

It introduces explicit descriptions of degenerate spectral curves in weak and strong coupling regimes, linking them to well-known integrable models and proving some open conjectures.

Findings

Weak coupling yields trigonometric Calogero-Moser and Toda models.

Strong coupling corresponds to solitonic degenerations.

Explicit formulas for coupling constants and superpotentials.

Abstract

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.