论文标题
四分之一bps状态，多对称功能和设置分区
Quarter-BPS states, multi-symmetric functions and set partitions
论文作者
论文摘要
我们为$ \ Mathcal {n} = 4 $ sym在弱耦合的$ \ u（n）$ gauge组中为$ \ mathcal {n} = 4 $ sym提供了一般全体形态四分之一bps运营商的构造。该结构采用Möbius倒置公式进行固定分区，应用于多对称函数，以及对称组的组代数中的计算。我们提出了一种计算算法，该算法在全体形态操作员空间上为物理内部产品产生正交基础。该基础由$ u（2）$ Young图，$ u（n）$ Young图和附加多余的多重性标签标记。我们描述了四分之一BPS状态的精度计数结果，这些结果有望从大量巨型重力中的双重计算中重现，包括在四分之一BPS扇区内的对称性相关的球体和广告巨头。在情况下，$ n \ leq n $（$ n $是复合操作员的维度），使用多对称功能和$ u（2）$ clebsch-gordan系数是分析性的。 BPS运算符的计数和相关器可以基于置换代数的二维拓扑字段理论编码，并配备适当的缺陷。
We give a construction of general holomorphic quarter BPS operators in $ \mathcal{N}=4$ SYM at weak coupling with $U(N)$ gauge group at finite $N$. The construction employs the Möbius inversion formula for set partitions, applied to multi-symmetric functions, alongside computations in the group algebras of symmetric groups. We present a computational algorithm which produces an orthogonal basis for the physical inner product on the space of holomorphic operators. The basis is labelled by a $U(2)$ Young diagram, a $U(N)$ Young diagram and an additional plethystic multiplicity label. We describe precision counting results of quarter BPS states which are expected to be reproducible from dual computations with giant gravitons in the bulk, including a symmetry relating sphere and AdS giants within the quarter BPS sector. In the case $n \leq N$ ($n$ being the dimension of the composite operator) the construction is analytic, using multi-symmetric functions and $U(2)$ Clebsch-Gordan coefficients. Counting and correlators of the BPS operators can be encoded in a two-dimensional topological field theory based on permutation algebras and equipped with appropriate defects.
