Bestiary of 6D (1, 0) SCFTs: Nilpotent orbits and anomalies

Many six-dimensional (1, 0) superconformal field theories (SCFTs) are known to fall into families labeled by nilpotent orbits of certain simple Lie algebras. For each of the three infinite series of such families, we show that the anomalies for the continuous zero-form global symmetries of a theory labelled by a nilpotent orbit <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>O</a:mi></a:math> of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi mathvariant="fraktur">g</c:mi></c:math> can be determined from the anomalies of the theory associated to the trivial nilpotent orbit (the parent theory), together with the data of <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mi>O</f:mi></f:math>. In particular, knowledge of the tensor branch field theory is bypassed completely. We show that the known anomalies, previously determined from the geometric/atomic construction, are reproduced by analyzing the Nambu-Goldstone modes inside of the moment map associated to the <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mi mathvariant="fraktur">g</h:mi></h:math> flavor symmetry of the parent SCFT. This provides further evidence for the physics underlying the labeling of the SCFTs by nilpotent orbits. We remark on some consequences, such as the reinterpretation of the 6D <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>a</k:mi></k:math>-theorem for such SCFTs in terms of group theory.