论文标题
箭仪理论和符号奇异
Quiver gauge theories and symplectic singularities
论文作者
论文摘要
Braverman，Finkelberg和Nakajima最近对大型$ 3D $ \ $ \ MATHCAL {N} = 4 $量规理论的库仑分支进行了数学结构，为具有Poisson结构的代数品种。他们猜想这些品种具有符合性的奇异性。我们确认了所有无环或多个边缘的所有颤抖理论的猜想，这特别意味着相应的库仑分支具有有限的许多合成性叶子和理性的戈伦斯坦奇异性。我们还提供了一个标准，以证明任何特定的库仑分支都具有符号奇异性，并讨论了我们的结果可能扩展到具有循环和/或多个边缘的Quivers。
Braverman, Finkelberg and Nakajima have recently given a mathematical construction of the Coulomb branches of a large class of $3d$ $\mathcal{N} =4$ gauge theories, as algebraic varieties with Poisson structure. They conjecture that these varieties have symplectic singularities. We confirm this conjecture for all quiver gauge theories without loops or multiple edges, which in particular implies that the corresponding Coulomb branches have finitely many symplectic leaves and rational Gorenstein singularities. We also give a criterion for proving that any particular Coulomb branch has symplectic singularities, and discuss the possible extension of our results to quivers with loops and/or multiple edges.
