The Strong-Coupling Spectrum of the Seiberg-Witten Theory

Abstract

We carefully study the global structure of the solution of the $N=2$ supersymmetric pure Yang-Mills theory with gauge group $SU(2)$ obtained by Seiberg and Witten. We exploit its ${\mathbf{Z}}_2$-symmetry and describe the curve in moduli space where BPS states can become unstable, separating the strong-coupling from the weak-coupling region. This allows us to obtain the spectrum of stable BPS states in the strong-coupling region: we prove that only the two particles responsible for the singularities of the solution (the magnetic monopole and the dyon of unit electric charge) are present in this region. Our method also permits us to very easily obtain the well-known weak-coupling spectrum, without using semi-classical methods. We discuss how the BPS states disintegrate when crossing the border from the weak to the strong-coupling region.

19 pages, uses PHYZZX, references changed and minor corrections, version published in Nuclear Physics B

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• The Vacuum Structure of N=2 SuperQCD with Classical Gauge Groups
• Curves of Marginal Stability and Weak and Strong-Coupling BPS Spectra in $N=2$ Supersymmetric QCD
• Duality in N=2 SUSY SU(2) Yang-Mills Theory: A pedagogical introduction to the work of Seiberg and Witten

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