nLab Seiberg duality

under construction

Idea

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 flavors and $SU(N_c)$ gauge group for

$$N_f \gt N_c +1$$

with solitons in a theory of $N_f$ quark flavors and gauge group $SU(\tilde N_c)$, where

$$\tilde N_c = N_f - N_c \,.$$

Properties

Realization in string theory

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.

• Amihay Hanany, 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.

Formalization by derived quiver categories

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)

Examples

Toric duality

Toric Duality is Seiberg duality for $N=1$ theories with toric moduli spaces.

• Bo Feng, Amihay Hanany, Yang-Hui He, D-brane gauge theories from toric singularities and toric duality, Nucl. Phys. B 595 (2001) 165 (arXiv:hep-th/0003085)

• Chris Beasley, M. Ronen Plesser, Toric duality is Seiberg duality, J. High Energy Phys. 12 (2001) 001 (hep-th/0109053)

• Bo Feng, Amihay Hanany, Yang-Hui He, Phase structure of D-brane gauge theories and toric duality , J. High Energy Phys. 08 (2001) 040 (hep-th/0104259)

• Bo Feng, Amihay Hanany, Yang-Hui He, Angel Uranga, Toric duality as Seiberg duality and brane diamonds, J. High Energy Phys. 12 (2001) 035 (hep-th/0109063)

• Bo Feng, S. Franco, Amihay Hanany, Yang-Hui He, Unhiggsing the del Pezzo, J. High Energy Phys. 08 (2003) 058 (hep-th/0209228)

• S. Franco and Amihay Hanany, Toric duality, Seiberg duality and Picard-Lefschetz transformations , Fortschr. Phys. 51 (2003) 738 (hep-th/0212299)

From D-branes on del Pezzo singularities

• Christopher 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)

For exceptional gauge groups

Seiberg duality for gauge groups which are exceptional Lie groups:

• Jacques Distler, Andreas Karch, $N=1$ Dualities for Exceptional Gauge Groups and Quantum Global Symmetries (arXiv:hep-th/9611088)

But see

• Peter Cho, Moduli in Exceptional SUSY Gauge Theories (arXiv:hep-th/9712116)

Chiral and non-chiral duals

• P. Pouliot, Chiral Duals of Non-Chiral SUSY Gauge Theories (arXiv:hep-th/9507018)

Duality cascade

Due to

• Igor Klebanov, Matthew Strassler, Supergravity and a Confining Gauge Theory: Duality Cascades and $\chi$SB-Resolution of Naked Singularities (arXiv)

A review is in

• Matthew Strassler, The Duality Cascade (arXiv:hep-th/0505153)

Discussion in connection with non-conformal variants of AdS/CFT is in

• Eduardo Conde, Jérôme Gaillard, Carlos Núñez, Maurizio Piai, Alfonso V. Ramallo, Towards the string dual of tumbling and cascading gauge theories (arXiv:1112.3346)

With few supercharges

• 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

• Adi Armoni, Two Examples of Seiberg Duality in Gauge Theories With Less Than Four Supercharges (pdf)

Related entries

• quiver gauge theory

duality in physics

• S-duality

  • electric-magnetic duality

    • Montonen-Olive duality

  • Seiberg duality

  • geometric Langlands duality

References

Original articles

The original article is

• Nathan Seiberg, Electric-Magnetic Duality in Supersymmetric Non-Abelian Gauge Theories (arXiv:hep-th/9411149)

The “cascade” of Seiberg dualities is due to

• Igor Klebanov, Matthew Strassler, Supergravity and a Confining Gauge Theory: Duality Cascades and $\chi$SB-Resolution of Naked Singularities (arXiv:hep-th/0007191)

Lectures and reviews

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

• Philip Argyres, Introduction to supersymmetry (pdf)