Supersymmetric D3 brane action in AdS_5 x S^5
  We find the space-time supersymmetric and kappa-invariant action for a D3-brane propagating in the AdS_5 x S^5 background. As in the previous construction of the fundamental string action in this maximally supersymmetric string vacuum the starting point is the corresponding superalgebra su(2,2|4). We comment on the super Yang-Mills interpretation of the gauge-fixed form of the action. 
R.R. Metsaev and A.A. Tseytlin