The algebra of flat currents for the string on AdS 5 × S 5 in the light - cone gauge

We continue the program initiated in hep-th/0411200 and calculate the algebra of the flat currents for the string on AdS 5 × S 5 background in the light-cone gauge with κ symmetry fixed. We find that the algebra has a closed form and that the non-ultralocal terms come with a weight factor e φ(σ) that depends on the radial AdS 5 coordinate. Based on results in two-dimensional sigma models coupled to gravity via the dilaton field, this suggests that the algebra of transition matrices in the present case is likely to be unam-bigous.