Superconformal Actions in Killing Gauge

The classical superconformal actions of branes in adS superspaces have a closed form depending on a matrix $M^2$ quadratic in fermions, as found in hep-th/9805217. One can gauge-fix the local $\kappa$-symmetry using the Killing spinors of the brane in the bulk. We show that in such gauges the superconformal actions are simplified dramatically since $M^2=0$ in all cases. The relation between classical and gauge-fixed actions for these theories reflects the relation between the full superconformal algebra and its supersolvable subalgebra.