N=4 holographic determinism?

AdS/CFT says that N=4 super-Yang-Mills is equal to the IIB string on AdS₅ x S⁵, and Arkani-Hamed et al are also constructing a twistorial formulation of the theory in which “locality”, “unitarity”, “gauge symmetry” etc are all replaced by a new set of concepts.

Now I want to mention a very intriguing possibility. For many years, Gerard ‘t Hooft has been pushing the idea that you could reconstruct quantum field theory from a cellular automaton, possibly in a lower number of dimensions. In his latest paper, he actually claims a “duality” between a certain C.A. and a free bosonic field theory in 1+1 dimensions. It has something to do with combinations of eigenvalues of operators on a special lattice of points – these points are the “cells”, and the combinations are the states of the cells.

It would be an interesting project to extend this work in the direction of the IIB worldsheet theory which produces the N=4 theory.