Antoine Bourget, Andrew Dancer, Julius F. Grimminger, Amihay Hanany, Frances Kirwan, Zhenghao Zhong
We propose quivers for Coulomb branch constructions of universal implosions for orthogonal and symplectic groups, extending the work on special unitary groups in arXiv:2004.09620. The quivers are unitary-orthosymplectic as opposed to the purely unitary quivers in the A-type case. Where possible we check our proposals using Hilbert series techniques.
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We propose magnetic quivers for partial implosion spaces. Such partial implosions involve a choice of parabolic subgroup, with the Borel subgroup corresponding to the standard implosion. In the subregular case we test the conjecture by verifying that reduction by the Levi group gives the appropriate nilpotent orbit closure. In the case of a parabolic corresponding to a hook diagram we are also able to carry out this verification provided we work at nonzero Fayet-Iliopoulos parameters.
Orthosymplectic Quotient Quiver Subtraction II: Framed Quivers
本文为带框架的正交辛箭图引入商箭图减法技术，通过规范固定红外库仑分支对称性子群并完全希格斯化，为所有经典群提供商箭图，并指出带框架与不带框架过程不同。
We investigate orthosymplectic quivers that take the shape of D-type and B-type Dynkin diagrams. The D-type orthosymplectic quivers explored here contain a balanced "fork", i.e., a balanced subquiver with a D-type bifurcation, whereas the B-type orthosymplectic quivers are obtained by folding the D-type quivers. The Coulomb branches of these quivers are products of two moduli spaces. In the second part, the relevant orthosymplectic quivers are shown to emerge as magnetic quivers for brane configurations involving ON$^0$ planes. Notably, the appearance of ON$^0$ plane clarifies the product natu…
Folding identical legs of a simply-laced quiver creates a quiver with a non-simply laced edge. So far, this has been explored for quivers containing unitary gauge groups. In this paper, orthosymplectic quivers are folded, giving rise to a new family of quivers. This is realised by intersecting orientifolds in the brane system. The monopole formula for these non-simply laced orthosymplectic quivers is introduced. Some of the folded quivers have Coulomb branches that are closures of minimal nilpotent orbits of exceptional algebras, thus providing a new construction of these fundamental moduli sp…
We study the moduli space of 3d $\mathcal{N}=4$ quiver gauge theories with unitary, orthogonal and symplectic gauge nodes, that fall into exceptional sequences. We find that both the Higgs and Coulomb branches of the moduli space factorise into decoupled sectors. Each decoupled sector is described by a single quiver gauge theory with only unitary gauge nodes. The orthosymplectic quivers serve as magnetic quivers for 5d $\mathcal{N}=1$ superconformal field theories which can be engineered in type IIB string theories both with and without an O5 plane. We use this point of view to postulate the d…
Orthosymplectic Quotient Quiver Subtraction
本文提出正交辛商箭图减法技术，推导了多类群的正交辛商箭图，将其应用于幂零轨道闭包磁箭图并得到新的库仑分支构造，还为两类6d N=(1,0)理论找到了磁箭图与膜系统，提供了强相互作用M5膜动力学的微扰拉格朗日实现。
Supersymmetric Sp(k) quantum chromodynamics with 8 supercharges in space-time dimensions 3 to 6 can be realised by two different Type II brane configurations in the presence of orientifolds. Consequently, two types of magnetic quivers describe the Higgs branch of the Sp(k) SQCD theory. This is a salient example of a general phenomenon: a given hyper-Kahler Higgs branch may admit several magnetic quiver constructions. It is then natural to wonder if these different magnetic quivers, which are described by 3d N=4 theories, are dual theories. In this work, the unitary and orthosymplectic magnetic…
We study the Higgs branch of 5d superconformal theories engineered from brane webs with orientifold five-planes. We propose a generalization of the rules to derive magnetic quivers from brane webs pioneered in arXiv:2004.04082, by analyzing theories that can be described with a brane web with and without O5 planes. Our proposed magnetic quivers include novel features, such as hypermultiplets transforming in the fundamental-fundamental representation of two gauge nodes, antisymmetric matter, and $\mathbb{Z}_2$ gauge nodes. We test our results by computing the Coulomb and Higgs branch Hilbert se…
For any gauge theory, there may be a subgroup of the gauge group which acts trivially on the matter content. While many physical observables are not sensitive to this fact, the identification of the precise gauge group becomes crucial when the magnetic spectrum of the theory is considered. This question is addressed in the context of Coulomb branches for $3$d $\mathcal{N}=4$ quiver gauge theories, which are moduli spaces of dressed monopole operators. Since monopole operators are characterized by their magnetic charge, the identification of the gauge group is imperative for the determination o…
A Pathway to Decay and Fission of Orthosymplectic Quiver Theories
提出一种提取正交辛3d N=4 quiver规范理论Coulomb branch Hasse图的算法，系统预测Higgsing产生的后裔理论及辛奇点分层结构，并通过3d mirror与高维SCFT的Higgsing流验证，揭示了新型Higgsing模式。
Orthosymplectic Chern-Simons Matter Theories: Global Forms, Dualities, and Vacua
本文提出了一种磁弦框架，用于研究具有$\mathcal{N} \geq 3$超对称性的三维正交辛Chern-Simons物质理论的最大分支，这些分支源于IIB膜设定中的O3平面。通过膜运动提取这些分支，得到正交辛$\mathcal{N}=4$磁弦，其Coulomb分支与感兴趣的模空间匹配。通过超对称指标、希尔伯特级数和 fugacity 映射确定全局规范群数据。分析具有探索性，突显了若干细微特征。特别是，磁弦被提出作为多种示例中最大分支的预测。
Orthosymplectic Quivers: Indices, Hilbert Series, and Generalised Symmetries
研究3d N=4正交辛有向图规范理论中的广义全局对称性，利用超共形指标识别D8分类对称性网络，并改进计算SO(N)规范理论Coulomb分支希尔伯特级数的方法，考虑离散零形式对称性和磁性对称性。
We study the Higgs branch of the SCFT limit of 5d SO(6) and SO(8) gauge theory with hypermultiplets in the spinor and vector representations. In the case of SO(6) gauge theories, we contrast the magnetic quivers obtained with those of SU(4) gauge theory with hypermultiplets in the fundamental and second rank antisymmetric representations. Since SU(4) gauge theories admit several different values of the Chern-Simons level, we make some observations about how to distinguish those theories from the brane webs of the SO(6) theories. In the case of SO(8) gauge theories, we use SO(8) triality to pro…
Orthosymplectic Donaldson-Thomas theory
本文构造并研究了线性范畴中计数正交和辛对象的 Donaldson-Thomas 不变量，推广了通常的 GL(n) 情形，利用动机 Hall 模定义并证明了墙交叉公式，并应用于 Calabi-Yau 三维流形、自对偶箭图及代数曲面上的 Vafa-Witten 不变量。
An exceptionally simple family of Orthosymplectic 3d $\mathcal{N}=4$ rank-0 SCFTs
本文研究了一族三维 N=4 秩-0 正交辛箭图规范理论，其希格斯分支全部平凡，库仑分支可分解为已知模空间乘积，并据此探讨了三维镜像、秩-0 四维 N=2 SCFT 与辛对偶性的联系。
The ABCDEF's of Matrix Models for Supersymmetric Chern-Simons Theories
本文考虑了N = 3的超对称Chern-Simons规范理论，它具有乘积酉群和正交辛群，具有双基本场和基本场.本文利用Kapustin-Willett-Yaakov矩阵模型研究了S^3上的配分函数。鞍点方程在一个大的N限制导致的约束，长程之间的本征值的力量必须取消，由此产生的非线性理论是仿射Dynkin型。我们引入了一个折叠/展开技巧，让我们，在大N矩阵模型的水平上，（i）映射与正交辛群的箭图与酉群，和（ii）获得非简单的花边箭图从相应的简单花边箭图使用Z_2外自同构。在弦论中描述了箭图的膜构型，折叠/展开被解释为定向折叠和轨道折叠平面的加法/减法。我们还将U（N）算符理论与具有Stieltjes-Wigert型势的仿射ADE算符矩阵模型联系起来，并从3 + 1维的Seiberg对偶导出了2 + 1维的广义Seiberg对偶.
In this note we construct magnetic quivers for the known rank-2 four dimensional $\mathcal{N}=2$ superconformal field theories. For every rank-1 theory one can find a unitary magnetic quiver; we observe that this is no longer possible at rank 2. Our list of magnetic quivers necessarily includes orthosymplectic quivers, in addition to unitary ones, of both the simply and non-simply laced variety. Using quiver subtraction, one can compute Higgs branch Hasse diagrams and compare with the results obtained via other methods finding nearly perfect agreement.
Spin(N) Magnetic Quivers
该研究为含旋量超多重态的5维N=1 Spin(N)规范理论引入新磁性箭图，拓展了正交辛极小箭图理论，其构造可实现非单秩幂零轨道闭包对应的箭图。
Discrete Gauging of 6d SCFTs and Wreathed 3d $\mathcal{N}=4$ Quivers
研究6维(1,0)SCFT经ℤ₂Green-Schwarz自同构规范后的希格斯分支模空间，提出从6维构造读取味对称性的方法，并通过计算ℤ₂-花环型3维N=4磁箭图的库仑分支希尔伯特级数验证，同时给出确定这类正交辛箭图希尔伯特级数的方法。
$\mathrm{O}$/$\mathrm{SO}$ Gauge Groups, $BC$ Quivers and $O3$ Planes
本文研究含 O3 定向平面的膜系统中三维 N=4 正交辛规范理论的全局形式，提出利用 1/2D5-膜读取 O(2k) 与 SO(2k) 规范节点的规则，并给出联系库仑分支的恒等式及关于极大 DC-链上作用的猜想。
Magnetic Quivers, Higgs Branches, and 6d N=(1,0) Theories -- Orthogonal and Symplectic Gauge Groups
D型ALE奇点上的M5膜显示了各种引入额外的无质量自由度的现象。已知M5膜在D型奇点上断裂。当两个分数M5膜重合时，就会产生无张力弦。因此，这些系统不允许低能拉格朗日描述。针对M5膜上的6维N=（1，0）世界体积理论，真空模空间有两个分支，即张量多重态中的标量场或超多重态中的标量场获得非平凡的真空期望值.正如以前的工作所建议的那样，每当一个BPS弦变得无张力时，希格斯分支可能会发生剧烈的变化。最近，磁颤动被引入，旨在捕获张量分支任何点上的所有希格斯分支。在本文中，形式主义扩展到IIA型膜配置涉及O 6平面。由于6dN =（1，0）理论是由正交辛规范群构成的，因此必须证明在O 6平面存在时磁势的导出规则。这是通过分析一个单一的M5膜上的D-型奇点的6d理论，并推导出磁颤的有限和无限规范耦合希格斯分支从膜配置。所提出的推导规则的有效性得到了支持，通过推导相关的Hasse图。对于多个M5膜，本文的方法提供了所有的希格斯分支在任何点的张量分支的磁颤。特别地，我们发现了一个有趣的与SO（8）非Higgsable团簇有关的无限规范耦合跃迁。
Symmetry Mitosis and Hasse Diagram Diamonds: A Note on Brane Configurations with $\mathrm{ON}^{0}$ Planes
本文提出通过'对称分裂'方法解决含$\mathrm{ON}^{0}$平面的膜配置对称性问题，并构造了相关磁夸克及哈塞图。
The Higgs Branch of 6d (1,0) SCFTs & LSTs with DE-type SUSY Enhancement
本文研究了可增强至DE型6d (2,0)理论的6d (1,0) SCFTs和LSTs的Higgs分支。利用F理论几何工程与Type IIA膜描述导出磁夸克，并结合扩展夸克减法算法揭示了Higgs分支的辛叶状结构；同时提出“切片减法”规则，推测了缺乏磁夸克的E型理论的横向切片。
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