# nLab Seiberg duality

Contents

under construction

## Surveys, textbooks and lecture notes

#### Quantum field theory

functorial quantum field 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 $N_f$ 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)

### 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 $N=1$ theories with toric moduli spaces.

### 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:

But see

### Chiral and non-chiral duals

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

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

### 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)

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