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Seiberg-rWitten theory yields exact solutions for the quantum dynamics on the Coulomb branch of \(\mathcal N=2\) supersymmetric gauge theories and uncovers the phenomenon of wall-crossing. These developments enable a consistent realization of \(\mathcal N=2\) S-duality, even in situations where the BPS spectrum appears to lack the necessary symmetries. We begin with the Seiberg–Witten analysis of four-dimensional \(\mathcal N=2\) \(\mathfrak {su}(2)\) SYM theory, both in the pure case and with up to four fundamental hypermultiplets, before outlining its generalizations to other \(\mathcal N=2\) gauge theories. Our discussion follows the original works Seiberg and Witten (Nucl Phys B 426, 1994); Seiberg and Witten (Nucl Phys B 431, 1994); Donagi and Witten (Nucl Phys B 460:299–334, 1996) and key reviews Alvarez-Gaume and Hassan, Fortsch Phys 45:159–236, 1997; Lerche, AIP Conf Proc 419(1), 1998; D’Hoker and Phong, Lectures on supersymmetric Yang-Mills theory and integrable systems, 1999; Tachikawa, \(N=2\) supersymmetric dynamics for pedestrians, 2013, while more mathematically oriented perspectives are provided in Witten (Dynamics of quantum field theory, 1999); Freed (Commun Math Phys 203:31–52, 1999).

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Seiberg–Witten Theory

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  • 发表日期：

    2026年

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  • Clarence Kineider,
  • Georgios Kydonakis,
  • Eugen Rogozinnikov,
  • Valdo Tatitscheff,
  • Alexander Thomas

摘要

Seiberg-rWitten theory yields exact solutions for the quantum dynamics on the Coulomb branch of \(\mathcal N=2\) supersymmetric gauge theories and uncovers the phenomenon of wall-crossing. These developments enable a consistent realization of \(\mathcal N=2\) S-duality, even in situations where the BPS spectrum appears to lack the necessary symmetries. We begin with the Seiberg–Witten analysis of four-dimensional \(\mathcal N=2\) \(\mathfrak {su}(2)\) SYM theory, both in the pure case and with up to four fundamental hypermultiplets, before outlining its generalizations to other \(\mathcal N=2\) gauge theories. Our discussion follows the original works Seiberg and Witten (Nucl Phys B 426, 1994); Seiberg and Witten (Nucl Phys B 431, 1994); Donagi and Witten (Nucl Phys B 460:299–334, 1996) and key reviews Alvarez-Gaume and Hassan, Fortsch Phys 45:159–236, 1997; Lerche, AIP Conf Proc 419(1), 1998; D’Hoker and Phong, Lectures on supersymmetric Yang-Mills theory and integrable systems, 1999; Tachikawa, \(N=2\) supersymmetric dynamics for pedestrians, 2013, while more mathematically oriented perspectives are provided in Witten (Dynamics of quantum field theory, 1999); Freed (Commun Math Phys 203:31–52, 1999).