The Algebra & Geometry of Modern Physics

Class S_k theories are four-dimensional N=1 superconformal field theories (SCFTs) whose origin is supposed to be the C^2/Z_k orbifold of N=(2,0) theory in six dimensions by a Riemann surface compactification. We consider the 't Hooft anomalies, which are one of the most accessible physical quantities, of these theories. We show that the anomaly polynomial of the former is obtained from that of the latter by the integral over the Riemann surface, which gives a check of the statement above and interestingly leads to a proposal of the anomalies of strongly coupled N=1 SCFTs. This talk is based on the collaboration with I. Bah, A. Hanany, and Y. Tachikawa.