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Previous studies of the type IIB superstring in an ${AdS_5 \times S^5}$background are based on a description of the superspace geometry as thequotient space $PSU(2,2|4)/SO(4,1) \times SO(5)$. This paper develops analternative approach in which the Grassmann coordinates provide a nonlinearrealization of $PSU(2,2|4)$ based on the quotient space $PSU(2,2|4)/SU(2,2)\times SU(4)$, and the bosonic coordinates are described as a submanifold of$SU(2,2) \times SU(4)$. This formulation keeps all bosonic symmetries manifest,and it provides the complete dependence on the Grassmann coordinates in termsof simple analytic expressions. It is used to construct the superstringworld-sheet action in a form in which the $PSU(2,2|4)$ symmetry is manifest andkappa symmetry can be established. This formulation might have some advantagescompared to previous ones, but this remains to be demonstrated.

New Formulation of the Type IIB Superstring Action in $AdS_5 \times S^5$