On the fixing of the κ gauge symmetry on AdS and flat background:: The lightcone action for the type IIb string on AdS5 ⊗ S5

We explore all the possible ways of fixing the kappa symmetry for both branes and strings by means of a constant projector. We find that they can be classified according to their behaviour under Dime conjugation and conjugation. This latter controls the maximum power of the fermionic variables in which the (super)vielbein can be expanded while the former determines which states cannot be described in the gauge. In particular there exists an interesting class of projectors for which vielbein are at most quadratic in the fermionic variables. As an example we compute the action for the type IIb on a AdS(5) circle times S-5 background with a lightcone-like projector; this action reduces to the usual lightcone GS string action in the flat limit. (C) 2000 Elsevier Science B.V. All rights reserved.