Higgs Branch, Hyper-Kähler Quotient and Duality in SUSY N = 2 Yang–Mills Theories (original) (raw)

1997, International Journal of Modern Physics A

Low-energy limits of N=2 supersymmetric field theories in the Higgs branch are described in terms of a non-linear 4-dimensional σmodel on a hyperKähler target space, classically obtained as a hyper-Kähler quotient of the original flat hypermultiplet space by the gauge group. We review in a pedagogical way this construction, and illustrate it in various examples, with special attention given to the singularities emerging in the low-energy theory. In particular, we thoroughly study the Higgs branch singularity of Seiberg-Witten SU (2) theory with N f flavors, interpreted by Witten as a small instanton singularity in the moduli space of one instanton on R 4 . By explicitly evaluating the metric, we show that this Higgs branch coincides with the Higgs branch of a U (1) N=2 SUSY theory with the number of flavors predicted by the singularity structure of Seiberg-Witten's theory in the Coulomb phase. We find another example of Higgs phase duality, namely between the Higgs phases of U (N c ) N f flavors and U (N f − N c ) N f flavors theories, by using a geometric interpretation due to Biquard et al. This duality may be relevant for understanding Seiberg's conjectured duality N c ↔ N f − N c in N=1 SUSY SU (N c ) gauge theories. 1 antoniad@orphee.polytechnique.fr 2

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