论文标题
非骨质类型的库仑分支（与Gurbir Dhillon和Theo Johnson-Freyd的附录有关）
Coulomb branches of noncotangent type (with appendices by Gurbir Dhillon and Theo Johnson-Freyd)
论文作者
论文摘要
我们提出了一个$ 3D \ {\ Mathcal n} = 4 $量规理论的库仑分支的构造，该理论对应于选择连接的还原组$ g $和符号有限二二二次依赖性$ \ mathbf m $ $ g $的$ g $，以满足某些某些Anomaly Camelomaly Camelomaly Camelomaly Cancellation条件。这扩展了Arxiv的构造：1601.03586（假定$ {\ MathBf M} = {\ MathBf N} \ oplus {\ MathBf N}^*$ for Some Anterionaling $ \ Mathbf n $ of $ G $）。我们的构造经过符号群$ sp（2n）$的扭曲派生的satake类别中的某些“通用”环对象。该对象的构造使用Weil表示的分类版本；我们还计算了（扭曲的）派生的satake等效性下的该对象的图像，并表明它可以从S.Lysenko在$ \ peripatorName {bun} _ {sp（sp（2n）}}（{\ mathbb p}^1）$中通过某些radon变换而引入的theta-sheaf。我们还讨论了我们的构造在4维规程理论中的$ s $ duality的潜在数学构建中，以及（某些扩展）d.ben-zvi，y.sakellaridis和a.venkatesh的猜想。
We propose a construction of the Coulomb branch of a $3d\ {\mathcal N}=4$ gauge theory corresponding to a choice of a connected reductive group $G$ and a symplectic finite-dimensional reprsentation $\mathbf M$ of $G$, satisfying certain anomaly cancellation condition. This extends the construction of arXiv:1601.03586 (where it was assumed that ${\mathbf M}={\mathbf N}\oplus{\mathbf N}^*$ for some representation $\mathbf N$ of $G$). Our construction goes through certain "universal" ring object in the twisted derived Satake category of the symplectic group $Sp(2n)$. The construction of this object uses a categorical version of the Weil representation; we also compute the image of this object under the (twisted) derived Satake equivalence and show that it can be obtained from the theta-sheaf introduced by S.Lysenko on $\operatorname{Bun}_{Sp(2n)}({\mathbb P}^1)$ via certain Radon transform. We also discuss applications of our construction to a potential mathematical construction of $S$-duality for super-symmetric boundary conditions in 4-dimensional gauge theory and to (some extension of) the conjectures of D.Ben-Zvi, Y.Sakellaridis and A.Venkatesh.
