Six-dimensional superconformal field theories (SCFTs) hold a special place in Quantum Field Theory, both as isolated non-perturbative fixed points of the Renormalization Group, and as progenitors of a plethora of theories in lower dimensions. In this talk, I will (slowly) review the classification of 6d (1,0) SCFTs and their relations with geometry, and describe the algorithm to obtain their anomaly polynomial from which part of the protected conformal data can be extracted. A large class of theories can then be understood as originating from a few "parent theories" after giving a nilpotent vacuum expectation value to the moment-map operator. I will show that the anomaly polynomial of the resulting theories can be found solely in terms of group theory, without ever needing to refer to the geometric construction. In turn, this result has a very simple and purely field-theoretic interpretation as a consequence of Goldstone's theorem.
