论文标题
理性$ q $ - 系统，希格斯林和镜子对称性
Rational $Q$-systems, Higgsing and Mirror Symmetry
论文作者
论文摘要
理性$ Q $ - 系统是一种有效的方法，可以解决bethe ansatz方程用于量子整合旋转链。我们为由$ a _ {\ ell-1} $ QUIVER描述的通用bethe ansatz方程构建了有理$ q $ - 系统，其中包括具有多个动量携带节点，通用不均匀性，通用对斜twist和$ q $ $ $ $ $ $ $ $ $ $ $ $的模型。这样构建的有理$ Q $系统由两个分区指定。在伯特/量规通讯下，有理$ q $ - 系统是一对一的信件，与3d $ \ nathcal {n} = 4 $ Quiver量规理论的类型$ {t} _ {\boldsymbolρ}^{\boldsymbolρ}^{\boldsymbolσ} [su（n）$，也是相同的分配。这表明有理$ q $ - 系统是伯特/量规通信的一种自然语言，因为$ {t} _ {\boldsymbolρ}^{\boldsymbolσ} [su（n）] $理论易于翻译。例如，我们表明，希格斯和库仑分支希格辛对应于修改有理$ q $系统中的一个分区之一，同时保持另一个分区。同样，通过简单地交换两个分区，就可以根据有理$ q $系统实现镜像对称性 - 与$ {t} _ {\boldsymbolρ}^{\boldsymbolσ} [su（n）$一样。我们通过评估3D $ \ Mathcal {n} = 4 $ $ u（n）$ n = 1，\ ldots，5 $ 5 $的3d $ \ Mathcal {n} = 4 $ \ u（n）$ sqcd Theories，来体现有理$ q $系统的计算效率。
The rational $Q$-system is an efficient method to solve Bethe ansatz equations for quantum integrable spin chains. We construct the rational $Q$-systems for generic Bethe ansatz equations described by an $A_{\ell-1}$ quiver, which include models with multiple momentum carrying nodes, generic inhomogeneities, generic diagonal twists and $q$-deformation. The rational $Q$-system thus constructed is specified by two partitions. Under Bethe/Gauge correspondence, the rational $Q$-system is in a one-to-one correspondence with a 3d $\mathcal{N}=4$ quiver gauge theory of the type ${T}_{\boldsymbolρ}^{\boldsymbolσ}[SU(n)]$, which is also specified by the same partitions. This shows that the rational $Q$-system is a natural language for the Bethe/Gauge correspondence, because known features of the ${T}_{\boldsymbolρ}^{\boldsymbolσ}[SU(n)]$ theories readily translate. For instance, we show that the Higgs and Coulomb branch Higgsing correspond to modifying one of the partitions in the rational $Q$-system while keeping the other untouched. Similarly, mirror symmetry is realized in terms of the rational $Q$-system by simply swapping the two partitions - exactly as for ${T}_{\boldsymbolρ}^{\boldsymbolσ}[SU(n)]$. We exemplify the computational efficiency of the rational $Q$-system by evaluating topologically twisted indices for 3d $\mathcal{N}=4$ $U(n)$ SQCD theories with $n=1,\ldots,5$.
