arXiv 2312.050762023-12-08hep-th

关于3d $\mathcal{N}=2$ SQCD及其3d GLSM解释的新结果

New results on 3d $\mathcal{N}=2$ SQCD and its 3d GLSM interpretation

Cyril Closset, Osama Khlaif

备注：: 20 pages; a contribution to the proceedings of the GLSM@30 conference

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AI总结：

本文综述3d $\mathcal{N}=2$ SQCD红外物理新结果，利用3d GLSM将扭曲手征环联系于Grassmann流形QK，并提出Grothendieck线及K理论枚举不变量的两种计算途径。

摘要：

在本短文中，我们回顾了近期关于具有幺正规范群的3d $\mathcal{N}=2$ SQCD红外物理的一些新结果，特别是在存在非零Fayet–Iliopoulos参数且Chern–Simons能级取一般值的情形下。我们回顾了用于计算半BPS线缺陷的3d $\mathcal{N}=2$ 扭曲手征环的3d GLSM（也称为3d A模型）方法。对于特定的Chern–Simons能级值，该扭曲手征环可借助Grassmann流形的量子K理论（QK）得到简洁解释。我们提出了3d规范理论的一组新线缺陷，称为Grothendieck线，它们表示QK环中的等变Schubert类。特别地，我们表明，表示Schubert类等变Chern特征标之双Grothendieck多项式，在物理上作为某些箭袋超对称量子力学的Witten指标出现。我们还解释了利用3d GLSM方法计算K理论枚举不变量的两种不同方式。本综述文章是对2023年5月在Simons几何与物理中心举行的GLSM@30会议论文集的贡献。

英文摘要：

In this note, we review some new results we recently obtained about the infrared physics of 3d $\mathcal{N}=2$ SQCD with a unitary gauge group, in particular in the presence of a non-zero Fayet-Iliopoulos parameter and with generic values of the Chern-Simons levels. We review the 3d GLSM (also known as 3d A-model) approach to the computation of the 3d $\mathcal{N}=2$ twisted chiral ring of half-BPS lines. For particular values of the Chern-Simons levels, this twisted chiral ring has a neat interpretation in terms of the quantum K-theory (QK) of the Grassmannian manifold. We propose a new set of line defects of the 3d gauge theory, dubbed Grothendieck lines, which represent equivariant Schubert classes in the QK ring. In particular, we show that double Grothendieck polynomials, which represent the equivariant Chern characters of the Schubert classes, arise physically as Witten indices of certain quiver supersymmetric quantum mechanics. We also explain two distinct ways how to compute K-theoretic enumerative invariants using the 3d GLSM approach. \textit{This review article is a contribution to the proceedings of the GLSM@30 conference, which was held in May 2023 at the Simons Center for Geometry and Physics.}

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