Notes on worldvolume supersymmetries for D-branes on AdS₅ X S⁵ background

We revisit the 1/2-BPS D-branes on the AdS$_5\times$S$^5$ background. Based only on the classification of 1/2-BPS D-branes obtained by the covariant open string description, we consider various purely static configurations of D-branes without any worldvolume flux on the AdS$_5\times$S$^5$ background. Under the covariant $\kappa$ symmetry fixing condition, we investigate which part the spacetime supersymmetries is preserved on the D-brane worldvolume and obtain the associated worldvolume supersymmetry transformation rules to leading order in the worldvolume fluctuating fields. It is shown that, for purely static configurations without any worldvolume flux, only the AdS type D-branes, in which the AdS radial direction is one of worldvolume coordinates, are 1/2-BPS.