A lattice Poisson algebra for the Pohlmeyer reduction of the AdS5 x S5 superstring

The Poisson algebra of the Lax matrix associated with the Pohlmeyer reduction of the AdS5×S5 superstring is computed from first principles. The resulting non-ultralocality is mild, which enables to write down a corresponding lattice quadratic Poisson algebra, a key step towards the integrable quantization of this theory from first principles