Type IIB superstring action in AdS_5 x S^5 background
  We construct the covariant kappa-symmetric superstring action for a type IIB superstring on AdS_5 x S^5 background. The action is defined as a 2d sigma-model on the coset superspace SU(2,2|4) / SO(4,1) x SO(5) and is shown to be the unique one that has the correct bosonic and flat space limits. 
R.R. Metsaev and A.A. Tseytlin