The GS String Action on AdS_5 x S^5
  We present a simple form of the Type IIB string action on $AdS_5\times S^5$. The result is achieved by fixing $\kappa$-symmetry in the Killing spinor gauge defined by the projector of the Killing spinor of the D3 brane. We show explicitly that in this gauge the superspace is greatly simplified which is the crucial ingredient for the simple string action. 
R. Kallosh and J. Rahmfeld