Toric Duality as Seiberg Duality and Brane Diamonds

TL;DR

This paper demonstrates that Toric Duality is equivalent to Seiberg duality in N=1 theories with toric moduli spaces, introduces new phases, and supports the diamond duality proposal with novel configurations.

Contribution

It establishes the equivalence of Toric Duality and Seiberg duality, introduces three new phases, and supports the diamond duality proposal with new configurations.

Findings

Toric Duality is Seiberg duality for N=1 toric theories.

Three new phases not obtainable by the inverse algorithm.

New diamond configurations for singularities.

Abstract

We use field theory and brane diamond techniques to demonstrate that Toric Duality is Seiberg duality for N=1 theories with toric moduli spaces. This resolves the puzzle concerning the physical meaning of Toric Duality as proposed in our earlier work. Furthermore, using this strong connection we arrive at three new phases which can not be thus far obtained by the so-called ``Inverse Algorithm'' applied to partial resolution of C^3/Z_3 x Z_3. The standing proposals of Seiberg duality as diamond duality in the work by Aganagic-Karch-L\"ust-Miemiec are strongly supported and new diamond configurations for these singularities are obtained as a byproduct. We also make some remarks about the relationships between Seiberg duality and Picard-Lefschetz monodromy.