  The Pohlmeyer reduced equations for strings moving only in the AdS subspace
of AdS_5 x S^5 have been used recently in the study of classical Euclidean
minimal surfaces for Wilson loops and some semiclassical three-point
correlation functions. We find an action that leads to these reduced
superstring equations. For example, for a bosonic string in AdS_n such an
action contains a Liouville scalar part plus a K/K gauged WZW model for the
group K=SO(n-2) coupled to another term depending on two additional fields
transforming as vectors under K. Solving for the latter fields gives a
non-abelian Toda model coupled to the Liouville theory. For n=5 we generalize
this bosonic action to include the S^5 contribution and fermionic terms. The
corresponding reduced model for the AdS_2 x S^2 truncation of the full AdS_5 x
S^5 superstring turns out to be equivalent to N=2 super Liouville theory. Our
construction is based on taking a limit of the previously found reduced theory
actions for bosonic strings in AdS_n x S^1 and superstrings in AdS_5 x S^5.
This new action may be useful as a starting point for possible quantum
generalizations or deformations of the classical Pohlmeyer-reduced theory. We
give examples of simple extrema of this reduced superstring action which
represent strings moving in the AdS_5 part of the space. Expanding near these
backgrounds we compute the corresponding fluctuation spectra and show that they
match the spectra found in the original superstring theory.
