论文标题
边界，垂缘和分解
Boundaries, Vermas, and Factorisation
论文作者
论文摘要
我们重新审视3D $ \ MATHCAL {n} = 4 $量学理论的超对称分区功能的分解。构建块是一类UV $ \ Mathcal {n} =（2,2）$边界条件的半球分区函数，它们模仿在存在实际质量和FI参数的情况下在Infinity中模仿孤立的真空。可以使用超对称定位来明确定义和计算这些构建块。我们表明，这些半球分区的某些限制功能与量化的希格斯和库仑分支手性环上的重量最低的Verma模块的特征相吻合。这导致了超级符号索引，扭曲索引和$ s^3 $分区功能的表达式。在途中，我们发现了边界的T Hooft异常，半球分区功能和Verma模块的最低权重之间的新连接。
We revisit the factorisation of supersymmetric partition functions of 3d $\mathcal{N}=4$ gauge theories. The building blocks are hemisphere partition functions of a class of UV $\mathcal{N}=(2,2)$ boundary conditions that mimic the presence of isolated vacua at infinity in the presence of real mass and FI parameters. These building blocks can be unambiguously defined and computed using supersymmetric localisation. We show that certain limits of these hemisphere partition functions coincide with characters of lowest weight Verma modules over the quantised Higgs and Coulomb branch chiral rings. This leads to expressions for the superconformal index, twisted index and $S^3$ partition function in terms of such characters. On the way we uncover new connections between boundary 't Hooft anomalies, hemisphere partition functions and lowest weights of Verma modules.
