Localization of twisted N=0,2$$ \mathcal{N}=\left(0,\;2\right) $$ gauged linear sigma models in two dimensions
Localization of twisted N=0,2$$ \mathcal{N}=\left(0,\;2\right) $$ gauged linear sigma models in two dimensions
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扭曲 N=0,2$$ mathcal{N}=left(0,;2 ight) $$ 二维测量线性西格玛模型的定位
DOI：
10.1007/jhep03(2016)070
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发表时间：
2015
影响因子：
5.4
通讯作者：
E. Sharpe
中科院分区：
文献类型：
--
作者：
Cyril Closset;W. Gu;B. Jia;E. Sharpe
本文利用超对称局部化方法研究了二维N= 0，2 $$ \mathcal{N}=\left（0，2\right）$$超对称规范线性sigma模型（GLSMs）.我们考虑N= 0，2 $$ \mathcal{N}=\left（0，\ 2\right）$$具有R-对称性的理论，它总是可以通过伪拓扑扭曲定义在弯曲空间上，同时保持平坦空间的两个超荷之一。对于N= 2，2 $$ \mathcal{N}=\left（2，\ 2\right）$$广义手征模的变形并保留一个库仑分支的广义手征模，我们考虑了A/2-扭曲并计算了某些伪手征算子的亏格-零关联函数，从而将最简单的扭曲手征环算子推广到N= 2，2 $$ \mathcal{N}=\left（2，\ 2\right）$$轨迹之外.这些相关函数可以用库仑分支上的某种留数运算来表示，推广了与N= 2，2 $$ \mathcal{N}=\left（2，2\right）$$轨迹相关的Jeffrey-Kirwan留数公式。对于阿贝尔GLSM，我们再现现有的结果与新的公式，使量子层上同调关系和其他属性的表现。对于非阿贝尔GLSMs，我们的方法导致新的结果。作为一个例子，我们简要讨论了格拉斯曼流形的量子层上同调。
A bstractWe study two-dimensional N=0,2$$ \mathcal{N}=\left(0,\ 2\right) $$ supersymmetric gauged linear sigma models (GLSMs) using supersymmetric localization. We consider N=0,2$$ \mathcal{N}=\left(0,\ 2\right) $$ theories with an R-symmetry, which can always be defined on curved space by a pseudo-topological twist while preserving one of the two supercharges of flat space. For GLSMs which are deformations of N=2,2$$ \mathcal{N}=\left(2,\ 2\right) $$ GLSMs and retain a Coulomb branch, we consider the A/2-twist and compute the genus-zero correlation functions of certain pseudo-chiral operators, which generalize the simplest twisted chiral ring operators away from the N=2,2$$ \mathcal{N}=\left(2,\ 2\right) $$ locus. These correlation functions can be written in terms of a certain residue operation on the Coulomb branch, generalizing the Jeffrey-Kirwan residue prescription relevant for the N=2,2$$ \mathcal{N}=\left(2,\ 2\right) $$ locus. For abelian GLSMs, we reproduce existing results with new formulas that render the quantum sheaf cohomology relations and other properties manifest. For non-abelian GLSMs, our methods lead to new results. As an example, we briefly discuss the quantum sheaf cohomology of the Grassmannian manifold.