Quotient quiver subtraction

IF 2.5 3区 物理与天体物理 Q2 PHYSICS, PARTICLES & FIELDS Nuclear Physics B Pub Date : 2024-10-31 DOI:10.1016/j.nuclphysb.2024.116731
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Abstract

We develop the diagrammatic technique of quiver subtraction to facilitate the identification and evaluation of the SU(n) hyper-Kähler quotient (HKQ) of the Coulomb branch of a 3d N=4 unitary quiver theory. The target quivers are drawn from a wide range of theories, typically classified as “good” or “ugly”, which satisfy identified selection criteria. Our subtraction procedure uses quotient quivers that are “bad”, differing thereby from quiver subtractions based on Kraft-Procesi transitions. The simple diagrammatic procedure identifies one or more resultant quivers, the union of whose Coulomb branches corresponds to the desired HKQ. Examples include quivers whose Coulomb branches are moduli spaces of free fields, closures of nilpotent orbits of classical and exceptional type, and slices in the affine Grassmanian. We calculate the Hilbert Series and Highest Weight Generating functions for HKQ examples of low rank. For certain families of quivers, we are able to conjecture HWGs for arbitrary rank. We examine the commutation relations between quotient quiver subtraction and other diagrammatic techniques, such as Kraft-Procesi transitions, quiver folding, and discrete quotients.
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商 quiver 减法
我们开发了 "颤子减法 "图解技术,以方便识别和评估 3d N=4 单元颤子理论库仑支的 SU(n) 超凯勒商(HKQ)。目标四元数来自广泛的理论,通常分为 "好的 "和 "丑的",它们都满足已确定的选择标准。我们的减法过程使用的是 "坏 "的引子,因此与基于卡夫-普罗切斯转换的引子减法不同。这个简单的图解程序可以识别出一个或多个结果四元组,其库仑分支的联合与所需的 HKQ 相对应。例子包括库仑分支为自由场模空间的四元组、经典和特殊类型的零势轨道闭包,以及仿射格拉斯曼中的切片。我们计算了低秩 HKQ 例子的希尔伯特数列和最高权重生成函数。对于某些四元组族,我们能够猜想任意秩的 HWG。我们研究了商quiver减法与其他图解技术(如卡夫-普罗切斯转换、quiver折叠和离散商)之间的换向关系。
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来源期刊
Nuclear Physics B
Nuclear Physics B 物理-物理:粒子与场物理
CiteScore
5.50
自引率
7.10%
发文量
302
审稿时长
1 months
期刊介绍: Nuclear Physics B focuses on the domain of high energy physics, quantum field theory, statistical systems, and mathematical physics, and includes four main sections: high energy physics - phenomenology, high energy physics - theory, high energy physics - experiment, and quantum field theory, statistical systems, and mathematical physics. The emphasis is on original research papers (Frontiers Articles or Full Length Articles), but Review Articles are also welcome.
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