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arXiv · hep-th/0403133

On Correspondences Between Toric Singularities and (p,q)-webs

Bo Feng·Yang-Hui He·Francis Lam
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Abstract

We study four-dimensional N=1 gauge theories which arise from D3-brane probes of toric Calabi-Yau threefolds. There are some standing paradoxes in the literature regarding relations among (p,q)-webs, toric diagrams and various phases of the gauge theories, we resolve them by proposing and carefully distinguishing between two kinds of (p,q)-webs: toric and quiver (p,q)-webs. The former has a one to one correspondence with the toric diagram while the latter can correspond to multiple gauge theories. The key reason for this ambiguity is that a given quiver (p,q)-web can not capture non-chiral matter fields in the gauge theory. To support our claim we analyse families of theories emerging from partial resolution of Abelian orbifolds using the Inverse Algorithm of hep-th/0003085 as well as (p,q)-web techniques. We present complex inter-relations among these theories by Higgsing, blowups and brane splittings. We also point out subtleties involved in the ordering of legs in the (p,q) diagram.

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Bo Feng, Yang-Hui He, Francis Lam. 2004-03-12. On Correspondences Between Toric Singularities and (p,q)-webs. https://doi.org/10.1016/j.nuclphysb.2004.08.048

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