标题： 从项链箭图到F定理、算符计数和T(U(N)) 显示英文标题

标题： From Necklace Quivers to the F-theorem, Operator Counting, and T(U(N))

摘要： 卡普斯汀、威尔特和雅科夫的矩阵模型是探索2+1维强相互作用超共形 Chern-Simons 理论性质的强大工具。 在本文中，我们使用这个矩阵模型来研究具有{\cal N}=3 超对称性和大 N 极限下的 U(N)^d 规范群的项链型图规范理论。在最简单的应用中，矩阵模型计算了规范理论在 S^3 上的自由能。 所提出的 F 定理指出，该量应在规约群流下减少。 我们证明对于这类流的一个简单类，我们的项链理论满足 F 定理。 我们还提供了一个矩阵模型本征值分布与左手算符数量之间的关系，我们推测该关系更普遍成立。 通过 AdS/CFT 对应性，因此矩阵模型鞍点自然地可以解释为 7 维三辛爱因斯坦空间及其某些 5 维子流形的体积。 作为最后的额外收获，我们的分析给出了 T(U(N)) 理论在 S^3 上的划分函数。 显示英文摘要

摘要： The matrix model of Kapustin, Willett, and Yaakov is a powerful tool for exploring the properties of strongly interacting superconformal Chern-Simons theories in 2+1 dimensions. In this paper, we use this matrix model to study necklace quiver gauge theories with {\cal N}=3 supersymmetry and U(N)^d gauge groups in the limit of large N. In its simplest application, the matrix model computes the free energy of the gauge theory on S^3. The conjectured F-theorem states that this quantity should decrease under renormalization group flow. We show that for a simple class of such flows, the F-theorem holds for our necklace theories. We also provide a relationship between matrix model eigenvalue distributions and numbers of chiral operators that we conjecture holds more generally. Through the AdS/CFT correspondence, there is therefore a natural dual geometric interpretation of the matrix model saddle point in terms of volumes of 7-d tri-Sasaki Einstein spaces and some of their 5-d submanifolds. As a final bonus, our analysis gives us the partition function of the T(U(N)) theory on S^3.