论文标题
高通道
Twisted Quasimaps and Symplectic Duality for Hypertoric Spaces
论文作者
论文摘要
我们研究了扭曲的准胶质的模量空间，以在三个维度的亚伯利亚超对称量规理论的希格斯分支中产生。这些参数的一般颤抖表示形式的构建块是$ \ mathbb {p}^1 $的等级一条带之间的地图，但要符合与箭量相关的稳定性条件，涉及束带和地图。我们表明，这些模量空间的奇异共同体学自然地与$ x $的“量化环空间”上的一对载体模块组合在一起，我们将其视为与无限多个物质领域相关理论的希格斯分支。我们构建了该理论的库仑分支，发现它是与$ x $相关的库仑分支的定期类似物。使用符号二元性的形式主义，我们根据周期性库仑分支上某个倾斜模块的特征来得出扭曲的准绝变不变的生成函数的表达式。当$ x $作为$ n $ -Step Flag Quiver的Abelianation出现时，我们为此生成功能提供了封闭的公式。
We study moduli spaces of twisted quasimaps to a hypertoric variety $X$, arising as the Higgs branch of an abelian supersymmetric gauge theory in three dimensions. These parametrise general quiver representations whose building blocks are maps between rank one sheaves on $\mathbb{P}^1$, subject to a stability condition, associated to the quiver, involving both the sheaves and the maps. We show that the singular cohomology of these moduli spaces is naturally identified with the Ext group of a pair of holonomic modules over the `quantized loop space' of $X$, which we view as a Higgs branch for a related theory with infinitely many matter fields. We construct the coulomb branch of this theory, and find that it is a periodic analogue of the coulomb branch associated to $X$. Using the formalism of symplectic duality, we derive an expression for the generating function of twisted quasimap invariants in terms of the character of a certain tilting module on the periodic coulomb branch. We give a closed formula for this generating function when $X$ arises as the abelianisation of the $N$-step flag quiver.
