nLab
Seiberg duality

under construction

Context

Physics

physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes


theory (physics), model (physics)

experiment, measurement, computable physics

Quantum field theory

String theory

Contents

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 fN_f quark falvors and SU(N c)SU(N_c) gauge group for

N f>N c+1 N_f \gt N_c +1

with solitons in a theory of N fN_f quark flavors and gauge group SU(N˜ c)SU(\tilde N_c), where

N˜ c=N fN c. \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. 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=1N = 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.

Examples

Toric duality

Toric Duality is Seiberg duality for N=1N=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].

From D-branes on del Pezzo singularities

  • 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)

For exceptional gauge groups

Seiberg duality for gauge groups which are exceptional Lie groups:

But see

Chiral and non-chiral duals

Duality cascade

Due to

A review is in

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

  • Eduardo Conde, Jerome 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=1N = 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)

duality in physics

References

Original articles

The original article is

The “cascade” of Seiberg dualities is due to

Lectures and reviews

Surveys and reviews include

See also section 22 of

  • Philip Argyres, Introduction to supersymmetry (pdf)

Revised on October 14, 2012 14:43:23 by Urs Schreiber (89.204.130.129)