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Seiberg duality (named after (Seiberg)) is a version of electric-magnetic duality in supersymmetric gauge theory.
For supersymmetric QCD it identifies in the infrared (long distance limit, and only there) the quarks and gluons in a theory with $N_f$ quark falvors and $SU(N_c)$ gauge group for
with solitons in a theory of $N_f$ quark flavors and gauge group $SU(\tilde N_c)$, where
Seiberg duality follows from phenomena in string theory, where gauge theories arise as the worldvolume theories of D-branes (geometric engineering of quantum field theory). Seiberg duality is obtained for gauge theories of D-branes that stretch between two NS5-branes. The duality operation corresponds to exchanging the two NS5-branes.
A. Hanany and Edward Witten, Type-IIB superstrings, BPS monopoles and three-dimensional gauge dynamics , Nucl. Phys. B 492 (1997) 152 (hep-th/9611230).
S. Elitzur, A. Giveon, D. Kutasov, E. Rabinovici and A. Schwimmer, Brane dynamics and $N = 1$ supersymmetric gauge theory, Nucl. Phys. B 505 (1997) 202 (hep-th/9704104)
See also string theory results applied elsewhere.
Seiberg duality is formalized by equivalences of derived categories of quiver representations.
David Berenstein, Michael Douglas, Seiberg Duality for Quiver Gauge Theories (arXiv:hep-th/0207027)
Subir Mukhopadhyay, Koushik Ray, Seiberg duality as derived equivalence for some quiver gauge theories (arXiv:hep-th/0309191)
Toric Duality is Seiberg duality for $N=1$ theories with toric moduli spaces.
Bo Feng, Amihay Hanany and Y.-H. He, D-brane gauge theories from toric singularities and toric duality, Nucl. Phys. B 595 (2001) 165 [hep-th/0003085].
C.E. Beasley and M.R. Plesser, Toric duality is Seiberg duality, J. High Energy Phys. 12 (2001) 001 [hep-th/0109053]. JHEP02(2004)070
Bo Feng, A. Hanany and Y.-H. He, Phase structure of D-brane gauge theories and toric duality , J. High Energy Phys. 08 (2001) 040 [hep-th/0104259].
Bo Feng, A. Hanany, Y.-H. He and A.M. Uranga, Toric duality as Seiberg duality and brane diamonds, J. High Energy Phys. 12 (2001) 035 [hep-th/0109063].
Bo Feng, S. Franco, A. Hanany and Y.-H. He, Unhiggsing the del Pezzo, J. High Energy Phys. 08 (2003) 058 [hep-th/0209228].
S. Franco and A. Hanany, Toric duality, Seiberg duality and Picard-Lefschetz transformations , Fortschr. Phys. 51 (2003) 738 [hep-th/0212299].
Christopher P. Herzog, Seiberg Duality is an Exceptional Mutation (arXiv:hep-th/0405118)
Subir Mukhopadhyay, Koushik Ray, Seiberg duality as derived equivalence for some quiver gauge theories Journal of High Energy Physics Volume 2004 JHEP02(2004)
Seiberg duality for gauge groups which are exceptional Lie groups:
But see
Due to
A review is in
Discussion in connection with non-conformal variants of AdS/CFT is in
a 3d Yang-Mills Chern-Simons theory with two supercharges ($N = 1$ SUSY in 3d)
(Adi Armoni, Amit Giveon, Dan Israel, Vasilis Niarchos, 2009
a non-supersymmetric theory in $4d§
(Adi Armoni, Dan Israel, Gregory Moraitis, Vasilis Niarchos, 2008).
Discussed in
The original article is
The “cascade” of Seiberg dualities is due to
Surveys and reviews include
Matthew Strassler, The Duality Cascade (2005) (arXiv:hep-th/0505153)
M. Chaichian, W.F. Chen, C. Montonen, New Superconformal Field Theories in Four Dimensions and N=1 Duality (arXiv:hep-th/0007240)
Flip Tanedo, Notes on Seibergology (pdf)
See also section 22 of