  We consider conformal and 't Hooft anomalies in six-dimensional ${\cal
N}=(1,0)$ superconformal field theories, focusing on those conformal anomalies
that determine the two- and three-point functions of conserved flavor and
$SU(2)_R$ currents, as well as stress tensors. By analyzing these correlators
in superspace, we explain why the number of independent conformal anomalies is
reduced in supersymmetric theories. For instance, non-supersymmetric CFTs in
six dimensions have three independent conformal $c$-anomalies, which determine
the stress-tensor two- and three-point functions, but in superconformal
theories the three $c$-anomalies are subject to a linear constraint. We also
describe anomaly multiplet relations, which express the conformal anomalies of
a superconformal theory in terms of its 't Hooft anomalies. Following earlier
work on the conformal $a$-anomaly, we argue for these relations by considering
the supersymmetric dilaton effective action on the tensor branch of such a
theory. We illustrate the utility of these anomaly multiplet relations by
presenting exact results for conformal anomalies, and hence current and
stress-tensor correlators, in several interacting examples.

High Energy Physics - Theory