1207.3612 (Gerard 't Hooft)

Discreteness and Determinism in Superstrings    [PDF]

Gerard 't Hooft

Ideas presented in two earlier papers are applied to string theory. It had been found that a deterministic cellular automaton in one space- and one time dimension can be mapped onto a bosonic quantum field theory on a 1+1 dimensional lattice. We now also show that a cellular automaton in 1+1 dimensions that processes only ones and zeros, can be mapped onto a fermionic quantum field theory in a similar way. The natural system to apply all of this to is superstring theory, and we find that all classical states of a classical, deterministic string propagating in a rectangular, D dimensional space-time lattice, with some boolean variables on it, can be mapped onto the elements of a specially chosen basis for a (quantized) D dimensional superstring. This string is moderated ("regularized") by a 1+1 dimensional lattice on its world sheet, which may subsequently be sent to the continuum limit. The space-time lattice in target space is not sent to the continuum, while this does not seem to reduce its physically desirable features, including Lorentz invariance.

View original: http://arxiv.org/abs/1207.3612