The off-shell symmetry algebra of the light-cone AdS₅×S⁵superstring

We analyse the supersymmetry algebra of a superstring propagating in the AdS 5 × 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 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 gauge theory.