Electric-Magnetic Duality in Supersymmetric Non-Abelian Gauge Theories

Electric-Magnetic Duality in Supersymmetric Non-Abelian Gauge Theories

20 Nov 1994 | N. Seiberg
N. Seiberg demonstrates electric-magnetic duality in N=1 supersymmetric non-Abelian gauge theories in four dimensions. He presents two different gauge theories (with different gauge groups and quark representations) that lead to the same long-distance physics. The quarks and gluons of one theory can be interpreted as solitons (non-Abelian magnetic monopoles) of the elementary fields of the other theory. The weak coupling region of one theory maps to the strong coupling region of the other. When one theory is Higgsed by a squark expectation value, the other theory becomes confined. Massless glueballs, baryons, and Abelian magnetic monopoles in the confined description are the weakly coupled elementary quarks (i.e., solitons of the confined quarks) in the dual Higgs description. Seiberg discusses the interacting non-Abelian Coulomb phase for SU(N_c) with 3N_c/2 < N_f < 3N_c, where the theory has a non-trivial fixed point. He argues that this phase is described by two dual theories: an SU(N_c) theory with N_f flavors and an SU(N_f - N_c) theory with N_f flavors and an additional gauge-invariant massless field. The quarks and gluons of one theory can be interpreted as solitons of the other theory. The duality helps understand the non-Abelian Coulomb phase, where the theory is self-dual. Seiberg also considers deformations of the theories, including flat directions and mass terms, which affect the gauge symmetry and the nature of the phases. He extends the analysis to SO(N_c) theories, showing that the duality generalizes to these theories as well. The duality interchanges the Higgs and confining phases, with the dual theories having the same global symmetries but different gauge groups. In the $SO(N_c)$ theories, Seiberg discusses the duality in more detail, including the effect of mass terms and flat directions. He shows that the duality generalizes to these theories, with the dual theories having the same gauge invariant operators and consistent anomaly conditions. The duality is further supported by the identification of operators and their transformation laws under discrete symmetries.N. Seiberg demonstrates electric-magnetic duality in N=1 supersymmetric non-Abelian gauge theories in four dimensions. He presents two different gauge theories (with different gauge groups and quark representations) that lead to the same long-distance physics. The quarks and gluons of one theory can be interpreted as solitons (non-Abelian magnetic monopoles) of the elementary fields of the other theory. The weak coupling region of one theory maps to the strong coupling region of the other. When one theory is Higgsed by a squark expectation value, the other theory becomes confined. Massless glueballs, baryons, and Abelian magnetic monopoles in the confined description are the weakly coupled elementary quarks (i.e., solitons of the confined quarks) in the dual Higgs description. Seiberg discusses the interacting non-Abelian Coulomb phase for SU(N_c) with 3N_c/2 < N_f < 3N_c, where the theory has a non-trivial fixed point. He argues that this phase is described by two dual theories: an SU(N_c) theory with N_f flavors and an SU(N_f - N_c) theory with N_f flavors and an additional gauge-invariant massless field. The quarks and gluons of one theory can be interpreted as solitons of the other theory. The duality helps understand the non-Abelian Coulomb phase, where the theory is self-dual. Seiberg also considers deformations of the theories, including flat directions and mass terms, which affect the gauge symmetry and the nature of the phases. He extends the analysis to SO(N_c) theories, showing that the duality generalizes to these theories as well. The duality interchanges the Higgs and confining phases, with the dual theories having the same global symmetries but different gauge groups. In the $SO(N_c)$ theories, Seiberg discusses the duality in more detail, including the effect of mass terms and flat directions. He shows that the duality generalizes to these theories, with the dual theories having the same gauge invariant operators and consistent anomaly conditions. The duality is further supported by the identification of operators and their transformation laws under discrete symmetries.
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