Counting Chiral Operators in Quiver Gauge Theories
Counting Chiral Operators in Quiver Gauge Theories
复制标题
计算箭袋规范理论中的手性算子
DOI：
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
A. Zaffaroni
中科院分区：
文献类型：
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作者：
Agostino Butti;D. Forcella;A. Hanany;David Vegh;A. Zaffaroni
我们详细讨论的问题，计数BPS规范不变算子的手征环的规范理论生活在D膜探测一般复曲面CY奇点。包括重子算符计数在内的生成函数的计算是基于场论中重子荷与CY奇点的Kahler模之间的关系。对规范理论和几何之间相互作用的研究表明，给定的几何扇区在场论中出现不止一次，导致了“多重性”的概念。我们详细解释了如何将一个D-膜的生成函数分解成不同的扇区，以及如何通过引入几何和异常重子荷来计算它们的多重性。体积指数仍然是从一个D-膜到任意N个D-膜的主要工具。给出了几个例子的显式公式，包括3/3，0和dP 1。
We discuss in detail the problem of counting BPS gauge invariant operators in the chiral ring of quiver gauge theories living on D-branes probing generic toric CY singularities. The computation of generating functions that include counting of baryonic operators is based on a relation between the baryonic charges in field theory and the Kahler moduli of the CY singularities. A study of the interplay between gauge theory and geometry shows that given geometrical sectors appear more than once in the field theory, leading to a notion of ``multiplicities". We explain in detail how to decompose the generating function for one D-brane into different sectors and how to compute their relevant multiplicities by introducing geometric and anomalous baryonic charges. The Plethystic Exponential remains a major tool for passing from one D-brane to arbitrary number N of D-branes. Explicit formulae are given for few examples, including 3/3, 0, and dP1.