标题： 三维拓扑场论与拿姆和公式 显示英文标题

标题： Three Dimensional Topological Field Theories and Nahm Sum Formulas

摘要： 已知二维共形场论（CFT）的一大类字符可以写成Nahm和的形式。在\cite{Zagier:2007knq}中，D. Zagier确定了一组Nahm和表达式，它们是在$SL(2,\mathbb{Z})$的一个同余子群下成为模函数的，并且可以被视为有理CFTs字符的候选者。受相同的公式出现在某些3d$\mathcal{N}=2$超对称规范理论的半指标中的观察启发，我们在低秩的3d$\mathcal{N}=2$阿贝尔Chern-Simons物质理论中进行了广泛的搜索，这些理论要么红外流到幺正拓扑场论（TFTs），要么$\mathcal{N}=4$零秩超共形场论（SCFTs）。这些都是3d理论中的特殊类别，预计它们的边界上支持有理和$C_2$余有限的Chiral代数。我们将我们的结果与Zagier的结果进行比较，并讨论了Nahm猜想可能的推广。 显示英文摘要

摘要： It is known that a large class of characters of 2d conformal field theories (CFTs) can be written in the form of a Nahm sum. In \cite{Zagier:2007knq}, D. Zagier identified a list of Nahm sum expressions that are modular functions under a congruence subgroup of $SL(2,\mathbb{Z})$ and can be thought of as candidates for characters of rational CFTs. Motivated by the observation that the same formulas appear as the half-indices of certain 3d $\mathcal{N}=2$ supersymmetric gauge theories, we perform a general search over low-rank 3d $\mathcal{N}=2$ abelian Chern-Simons matter theories which either flow to unitary TFTs or $\mathcal{N}=4$ rank-zero SCFTs in the infrared. These are exceptional classes of 3d theories, which are expected to support rational and $C_2$-cofinite chiral algebras on their boundary. We compare and contrast our results with Zagier's and comment on a possible generalization of Nahm's conjecture.