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With a motivation to find a 2-d Lorentz-invariant solution of the AdS_5 x S^5superstring we continue the study of the Pohlmeyer-reduced form of this theory.The reduced theory is constructed from currents of the superstring sigma modeland is classically equivalent to it. Its action is that ofG/H=Sp(2,2)xSp(4)/SU(2)^4 gauged WZW model deformed by an integrable potentialand coupled to fermions. This theory is UV finite and is conjectured to berelated to the superstring theory also at the quantum level. Expanded near thetrivial vacuum it has the same elementary excitations (8+8 massive bosonic andfermionic 2-d degrees of freedom) as the AdS_5 x S^5 superstring in thelight-cone gauge or near plane-wave expansion. In contrast to the superstringcase, the interaction terms in the reduced action are manifestly 2-d Lorentzinvariant. Since the theory is integrable, its S-matrix should be effectivelydetermined by the two-particle scattering. Here we explicitly compute thetree-level two-particle S-matrix for the elementary excitations of the reducedtheory. We find that this S-matrix has the same index structure and groupfactorization properties as the superstring S-matrix computed in hep-th/0611169but has simpler coefficients, depending only on the difference of tworapidities. While the gauge-fixed form of the reduced action has only thebosonic SU(2)^4 part of the PSU(2|2) x PSU(2|2) symmetry of the light-conesuperstring spectrum as its manifest symmetry we conjecture that it should alsohave a hidden fermionic symmetry that effectively interchanges bosons andfermions and which should guide us towards understanding the relation betweenthe two S-matrices.

Tree-level S-matrix of Pohlmeyer reduced form of AdS_5 x S^5 superstring theory