The off-shell symmetry algebra of the light-cone AdS5 x S5 superstring

We analyse the psu(2, 2 vertical bar 4) supersymmetry algebra of a superstring propagating in the AdS(5) x S-5 background in the uniform light-cone gauge. We consider the off-shell theory by relaxing the level-matching condition and take the limit of infinite light-cone momentum, which decompactifies the string world-sheet. We focus on the psu(2|2) circle plus psu(2 vertical bar 2) subalgebra which leaves the light-cone Hamiltonian invariant and show that it undergoes extension by a central element which is expressed in terms of the level-matching operator. This result is in agreement with the conjectured symmetry algebra of the dynamic S-matrix in the dual 4 gauge theory.