On the fixing of the kappa gauge symmetry on AdS and flat background: The lightcone action for the type IIb string on AdS(5) circle times S-5

We explore all the possible ways of fixing the kappa symmetry for both bran es and strings by means of a constant projector. We find that they can be c lassified according to their behaviour under Dime conjugation and conjugati on. This latter controls the maximum power of the fermionic variables in wh ich the (super)vielbein can be expanded while the former determines which s tates cannot be described in the gauge. In particular there exists an inter esting 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 o n a AdS(5) circle times S-5 background with a lightcone-like projector; thi s action reduces to the usual lightcone GS string action in the flat limit. (C) 2000 Elsevier Science B.V. All rights reserved.