Anomaly matching on the Higgs branch

We point out that we can almost always determine by the anomaly matching the full anomaly polynomial of a supersymmetric theory in 2d, 4d or 6d if we assume that its Higgs branch is the one-instanton moduli space of some group G. This method not only provides by far the simplest method to compute the central charges of known theories of this class, e.g. 4d E_6,7,8 theories of Minahan and Nemeschansky or the 6d E-string theory, but also gives us new pieces of information about unknown theories of this class.