论文标题
费米气体的通用级别理论和量子曲线的方法
Fermi gas approach to general rank theories and quantum curves
论文作者
论文摘要
众所周知，计算三维$ \ MATHCAL {n} = 4 $的分区函数的矩阵模型可以将圆形颤动图描述的超符合性的Chern-Simons理论写成，当所有节点均具有相等的等级时，可以将其作为理想费米气体的分区函数。我们扩展了这种方法以对变形理论进行排名。除费米气体因子外，所得的矩阵模型仅取决于相对等级的因素。我们发现，这种分解在显示与汉纳尼 - 理工过渡相关的双重理论的划分函数的平等方面起着关键作用。此外，我们表明，理想费米气体的密度矩阵的倒置可以简化并被视为量子曲线，就像没有等级变形的情况下一样。我们还使用我们的结果对四个节点理论发表评论。
It is known that matrix models computing the partition functions of three-dimensional $\mathcal{N}=4$ superconformal Chern-Simons theories described by circular quiver diagrams can be written as the partition functions of ideal Fermi gases when all the nodes have equal ranks. We extend this approach to rank deformed theories. The resulting matrix models factorize into factors depending only on the relative ranks in addition to the Fermi gas factors. We find that this factorization plays a critical role in showing the equality of the partition functions of dual theories related by the Hanany-Witten transition. Furthermore, we show that the inverses of the density matrices of the ideal Fermi gases can be simplified and regarded as quantum curves as in the case without rank deformations. We also comment on four nodes theories using our results.
