Motivated by a desire to find a useful 2d Lorentz-invariant reformulation of the AdS 5 × S 5 superstring world-sheet theory in terms of physical degrees of freedom we construct the "Pohlmeyerreduced" version of the corresponding sigma model. The Pohlmeyer reduction procedure involves several steps. Starting with a coset space string sigma model in the conformal gauge and writing the classical equations in terms of currents one can fix the residual conformal diffeomorphism symmetry and kappa-symmetry and introduce a new set of variables (related locally to currents but non-locally to the original string coordinate fields) so that the Virasoro constraints are automatically satisfied. The resulting equations can be obtained from a Lagrangian of a non-abelian Toda type: a gauged WZW model with an integrable potential coupled also to a set of 2d fermionic fields. A gauge-fixed form of the Pohlmeyer-reduced theory can be found by integrating out the 2d gauge field of the gauged WZW model. The small-fluctuation spectrum near the trivial vacuum contains 8 bosonic and 8 fermionic degrees of freedom with equal mass. We conjecture that the reduced model has world-sheet supersymmetry and is ultraviolet-finite. We show that in the special case of the AdS 2 × S 2 superstring model the reduced theory is indeed supersymmetric: it is equivalent to the N=2 supersymmetric extension of the sine-Gordon model.

For free-field theories associated with BRST first-quantized gauge systems, we identify generalized auxiliary fields and pure gauge variables already at the first-quantized level as the fields associated with algebraically contractible pairs for the BRST operator. Locality of the field theory is taken into account by separating the space-time degrees of freedom from the internal ones. A standard extension of the first-quantized system, originally developed to study quantization on curved manifolds, is used here for the construction of a firstorder parent field theory that has a remarkable property: by elimination of generalized auxiliary fields, it can be reduced both to the field theory corresponding to the original system and to its unfolded formulation. As an application, we consider the free higher-spin gauge theories of Fronsdal.