December 25, 2002
Toric Duality arises as an ambiguity in computing the quiver gauge theory living on a D3-brane which probes a toric singularity. It is reviewed how, in simple cases Toric Duality is Seiberg Duality. The set of all Seiberg Dualities on a single node in the quiver forms a group which is contained in a larger group given by a set of Picard-Lefschetz transformations. This leads to elements in the group (sometimes called fractional Seiberg Duals) which are not Seiberg Duality on a single node, thus providing a new set of gauge theories which flow to the same universality class in the Infra Red.
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This paper serves to elucidate the nature of toric duality dubbed in hep-th/0003085 in the construction for world volume theories of D-branes probing arbitrary toric singularities. This duality will be seen to be due to certain permutation symmetries of multiplicities in the gauged linear sigma model fields. To this symmetry we shall refer as ``multiplicity symmetry.'' We present beautiful combinatorial properties of these multiplicities and rederive all known cases of torica...
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We study four-dimensional N=1 gauge theories arising on D3-branes probing toric singularities. Toric dualities and flows between theories corresponding to different singularities are analyzed by encoding the geometric information into (p,q) webs. A new method for identifying global symmetries of the four-dimensional theories using the brane webs is developed. Five-dimensional theories are associated to the theories on the D3-branes by using (p,q) webs. This leads to a novel i...
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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 ...
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We show that not all $(2+1)$ dimensional toric phases are Seiberg-like duals. Particularly, we work out superconformal indices for the toric phases of Fanos ${\cal{C}}_3$, ${\cal{C}}_5$ and ${\cal{B}}_2$. We find that the indices for the two toric phases of Fano ${\cal{B}}_2$ do not match, which implies that they are not Seiberg-like duals. We also take the route of acting Seiberg-like duality transformation on toric quiver Chern-Simons theories to obtain dual quivers. We stu...
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