论文标题
对AGT信函的缓慢评论
A slow review of the AGT correspondence
论文作者
论文摘要
从从其6D来源开始对AGT对应的柔和方法开始，这些音符对直到2020年初的多个信件扩展的文献进行了广泛的（尽管浅）的调查。这是对2020年冬季学校Yrisw 2020的讲座的扩展文章，出现在Jphysa的特殊问题中。 S类是4D $ n = 2 $ supersymmetric量规的理论（从超级QCD到非拉格朗日理论）的宽类，通过在Riemann表面上的6d $ n =（2,0）$ super Conconformal Theories获得。这种6D的结构产生了类S级理论的库仑分支和塞伯格（Seiberg）的几何形状，几何形成了s偶尔，并导致AGT对应关系，其中许多类别的S级理论的可观察到等于2D CFT相关器。例如，4D $ n = 2 $ su（2）超宪法箭量理论的四个球分区函数等于主操作员的liouville CFT相关器。 Extensions of the AGT correspondence abound: asymptotically-free gauge theories and Argyres-Douglas theories correspond to irregular CFT operators, quivers with higher-rank gauge groups and non-Lagrangian tinkertoys such as $T_N$ correspond to Toda CFT correlators, and nonlocal operators (Wilson-'t Hooft loops, surface operators, domain walls) correspond to Verlinde networks,将主要运算符，编织和融合内核以及边界表面的riemann表面。
Starting with a gentle approach to the AGT correspondence from its 6d origin, these notes provide a wide (albeit shallow) survey of the literature on numerous extensions of the correspondence up to early 2020. This is an extended writeup of the lectures given at the Winter School YRISW 2020, to appear in a special issue of JPhysA. Class S is a wide class of 4d $N=2$ supersymmetric gauge theories (ranging from super-QCD to non-Lagrangian theories) obtained by twisted compactification of 6d $N=(2,0)$ superconformal theories on a Riemann surface. This 6d construction yields the Coulomb branch and Seiberg-Witten geometry of class S theories, geometrizes S-duality, and leads to the AGT correspondence, which states that many observables of class S theories are equal to 2d CFT correlators. For instance, the four-sphere partition function of a 4d $N=2$ SU(2) superconformal quiver theory is equal to a Liouville CFT correlator of primary operators. Extensions of the AGT correspondence abound: asymptotically-free gauge theories and Argyres-Douglas theories correspond to irregular CFT operators, quivers with higher-rank gauge groups and non-Lagrangian tinkertoys such as $T_N$ correspond to Toda CFT correlators, and nonlocal operators (Wilson-'t Hooft loops, surface operators, domain walls) correspond to Verlinde networks, degenerate primary operators, braiding and fusion kernels, and Riemann surfaces with boundaries.
