On correspondences between toric singularities and (p,q) webs

Article, Preprint English OPEN
Feng, B. ; He, Y. ; Lam, F. (2004)
  • Publisher: Elsevier
  • Related identifiers: doi: 10.1016/j.nuclphysb.2004.08.048
  • Subject: QC | High Energy Physics - Theory
    arxiv: Mathematics::Algebraic Geometry | Mathematics::Symplectic Geometry

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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