On gauge-fixed superbrane actions in AdS superbackgrounds

To construct actions for describing superbranes propagating in AdS×S superbackgrounds we propose a coset space realization of these superbackgrounds which results in a short polynomial fermionic dependence (up to the sixth power in Grassmann coordinates) of target superspace supervielbeins and superconnections. Gauge fixing κ-symmetry in a way compatible with a static brane solution further reduces the fermionic dependence down to the fourth power. Subtleties of consistent gauge fixing worldvolume diffeomorphisms and κ-symmetry of the superbrane actions are discussed.