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 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.
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