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

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