Pohlmeyer reduction of superstring sigma model

Motivated by a desire to find a useful 2d Lorentz-invariant reformulation of the AdS₅×S⁵ superstring world-sheet theory in terms of physical degrees of freedom we construct the “Pohlmeyer-reduced” 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 AdS₂×S² superstring model the reduced theory is indeed supersymmetric: it is equivalent to the N=2 supersymmetric extension of the sine-Gordon model.