On correspondences between toric singularities and (p,q)-webs
On correspondences between toric singularities and (p,q)-webs
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关于环面奇点与 (p,q)-网之间的对应关系
DOI：
10.1016/j.nuclphysb.2004.08.048
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发表时间：
2004
期刊：
影响因子：
--
通讯作者：
Francis Lam
中科院分区：
文献类型：
--
作者：
Bo Feng;Yang;Francis Lam
本文研究了由复曲面Calabi-Yau三重D3-膜探测产生的四维N=1规范理论。在文献中关于（p，q）-网、环面图和规范理论的各个相之间的关系存在一些悖论，我们通过提出并仔细区分两种（p，q）-网：环面和环面（p，q）-网来解决这些悖论。前者与复曲面图有一一对应关系，而后者可以对应于多规范理论。这种模糊性的关键原因是给定的π（p，q）-网不能捕获规范理论中的非手征物质场。为了支持我们的主张，我们分析家庭的理论出现的部分分辨率阿贝尔orbifolds使用逆算法的hep-th/0003085以及（p，q）-web技术。我们通过希格辛、爆破和膜分裂来展示这些理论之间复杂的相互关系。我们还指出了（p，q）图中腿的排序所涉及的微妙之处。
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 cannot 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.