Class S anomalies from M-theory inflow

We present a first principles derivation of the anomaly polynomials of 4d N=2 class S theories of type A_N-1 with arbitrary regular punctures, using anomaly inflow in the corresponding M-theory setup with N M5-branes wrapping a punctured Riemann surface. The labeling of punctures in our approach follows entirely from the analysis of the 11d geometry and G₄ flux. We highlight the applications of the inflow method to the AdS/CFT correspondence.