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Electric-magnetic duality, monopole condensation, and confinement in \(N=2\) supersymmetric Yang-Mills theory. (English) Zbl 0996.81510
Summary: We study the vacuum structure and dyon spectrum of \(N=2\) supersymmetric gauge theory in four dimensions, with gauge group SU(2). The theory turns out to have remarkably rich and physical properties which can nonetheless be described precisely; exact formulas can be obtained, for instance, for electron and dyon masses and the metric on the moduli space of vacua. The description involves a version of Olive-Montonen electric-magnetic duality. The “strongly coupled” vacuum turns out to be a weakly coupled theory of monopoles, and with a suitable perturbation confinement is described by monopole condensation.

MSC:
81T60 Supersymmetric field theories in quantum mechanics
11Z05 Miscellaneous applications of number theory
14H52 Elliptic curves
81T13 Yang-Mills and other gauge theories in quantum field theory
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