论文标题
$ \ mathcal {n} = 2^{*} $ Schur indices
$\mathcal{N}=2^{*}$ Schur indices
论文作者
论文摘要
我们发现4D $ \ MATHCAL {N} = 2^{*}的Schur指数的封闭式表达式具有通过Fermi-Gas公式进行任意等级的统一仪表组的Super Yang-Mills理论。它们可以作为与理想费米亚气体系统的光谱Zeta函数相关的年轻图表写成的总和。这些功能是根据扭曲的WeierStrass函数表示的，为准雅各比形式生成函数。这些索引位于kronecker theta函数产生的多项式环和包含准雅各比形式的多项式环的Weierstrass函数。宏伟的规范合奏允许另一种简单的精确形式作为无限系列。此外，我们发现未经饮用的Schur指数及其限制可以用组合对象的几种生成函数来表达，包括三角数的总和，一般性的分隔和分区总和。
We find closed-form expressions for the Schur indices of 4d $\mathcal{N}=2^{*}$ super Yang-Mills theory with unitary gauge groups for arbitrary ranks via the Fermi-gas formulation. They can be written as a sum over the Young diagrams associated with spectral zeta functions of an ideal Fermi-gas system. These functions are expressed in terms of the twisted Weierstrass functions, generating functions for quasi-Jacobi forms. The indices lie in the polynomial ring generated by the Kronecker theta function and the Weierstrass functions which contains the polynomial ring of the quasi-Jacobi forms. The grand canonical ensemble allows for another simple exact form of the indices as infinite series. In addition, we find that the unflavored Schur indices and their limits can be expressed in terms of several generating functions for combinatorial objects, including sum of triangular numbers, generalized sums of divisors and overpartitions.
