## Toric duality is seiberg duality

We study four N = 1 SU(N)6 gauge theories, with bi-fundamental chiral matter and a superpotential. In the infrared, these gauge theories all realize the low-energy world-volume description of N coincident D3-branes transverse to the complex cone over a del Pezzo surface dP3 which is the blowup of P2 at three generic points. Therefore, the four gauge theories are expected to fall into the same universality class — an example of a phenomenon that has been termed “toric duality”. However, little independent evidence has been given that such theories are infrared-equivalent. In fact, we show that the four gauge theories are related by the N = 1 duality of Seiberg, vindicating this expectation. We also study holographic aspects of these gauge theories. In particular we relate the spectrum of chiral operators in the gauge theories to wrapped D3-brane states in the AdS dual description. We finally demonstrate that the other known examples of toric duality are related by N = 1 duality, a fact which we conjecture holds generally.

### Duke Scholars

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## Related Subject Headings

- Nuclear & Particles Physics
- 5107 Particle and high energy physics
- 5106 Nuclear and plasma physics
- 4902 Mathematical physics
- 0206 Quantum Physics
- 0202 Atomic, Molecular, Nuclear, Particle and Plasma Physics
- 0105 Mathematical Physics

### Citation

*Journal of High Energy Physics*,

*5*(12), 1–37. https://doi.org/10.1088/1126-6708/2001/12/001

*Journal of High Energy Physics*5, no. 12 (January 1, 2001): 1–37. https://doi.org/10.1088/1126-6708/2001/12/001.

*Journal of High Energy Physics*, vol. 5, no. 12, Jan. 2001, pp. 1–37.

*Scopus*, doi:10.1088/1126-6708/2001/12/001.

## Published In

## DOI

## ISSN

## Publication Date

## Volume

## Issue

## Start / End Page

## Related Subject Headings

- Nuclear & Particles Physics
- 5107 Particle and high energy physics
- 5106 Nuclear and plasma physics
- 4902 Mathematical physics
- 0206 Quantum Physics
- 0202 Atomic, Molecular, Nuclear, Particle and Plasma Physics
- 0105 Mathematical Physics