Type IIB Green-Schwarz superstrings in AdS5 x S5 from the supercoset approach

We consider superstrings moving in the AdS5 x S 5 space-time and find their Green-Schwarz action using the supercoset approach based on the supergroup PSU(2, 2 vertical bar 4). We describe several parametrizations of the relevant supercoset and present the action in different κ-symmetry gauges. In particular, we discuss a gauge where all the fermionic coordinates corresponding to the conformal (S) supercharges are gauged away and also a light-cone type gauge where half of the Q and S supercoordinates are gauged away. The resulting action contains terms that are quadratic and quartic in fermions. In the flat-space limit, it reduces to the standard light-cone Green-Schwarz action. We comment on the possibility of fixing the bosonic light-cone gauge and of reformulating the action in terms of two-dimensional Dirac spinors