Toric Duality Is Seiberg Duality

TL;DR

This paper demonstrates that toric duality among certain N=1 gauge theories is actually a manifestation of Seiberg duality, providing evidence for their infrared equivalence and exploring holographic correspondences.

Contribution

It proves that four toric dual gauge theories are related by Seiberg duality, confirming their infrared equivalence and extending the understanding of toric duality as Seiberg duality.

Findings

The four gauge theories are related by Seiberg duality.

Spectrum of chiral operators matches wrapped D3-brane states.

Other examples of toric duality are also connected by N=1 duality.

Abstract

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 dP_3 which is the blowup of P^2 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.