Structure of anomalies of 4d SCFTs from M5-branes, and anomaly inflow

We study the 't Hooft anomalies of four-dimensional superconformal field theories that arise from M5-branes wrapped on a punctured Riemann surface. In general there are two independent contributions to the anomalies. There is a bulk term obtained by integrating the anomaly polynomial of the world-volume theory on the M5-branes over the Riemann surface; this contribution knows about the punctures only through its dependence on the Euler characteristic of the surface. The second set of contributions comes from local data at the punctures; these terms are independent from the bulk data of the surface. Using anomaly inflow in M-theory, we describe the general structure of the anomalies for cases when the four-dimensional theories preserve N=2 supersymmetry. We additionally discuss the anomalies corresponding to (p, q) punctures in N=1 theories.