Stable String Bit Models

Abstract

In string bit models, the superstring emerges as a very long chain of "bits", in which s fermionic degrees of freedom contribute positively to the ground state energy in a way to exactly cancel the destabilizing negative contributions of d=s bosonic degrees of freedom. We propose that the physics of string formation be studied nonperturbatively in the class of string bit models in which s>d, so that a long chain is stable, in contrast to the marginally stable (s=d=8) superstring chain. We focus on the simplest of these models with s=1 and d=0, in which the string bits live in zero space dimensions. The string bit creation operators are N X N matrices. We choose a Hamiltonian such that the large N limit produces string moving in one space dimension, with excitations corresponding to one Grassmann lightcone worldsheet field (s=1) and no bosonic worldsheet field (d=0). We study this model at finite N to assess the role of the large N limit in the emergence of the spatial dimension. Our results suggest that string-like states with large bit number M may not exist for N<(M-1)/2. If this is correct, one can have finite chains of string bits, but not continuous string, at finite N. Only for extremely large N can such chains behave approximately like continuous string, in which case there will also be the (approximate) emergence of a new spatial dimension. In string bit models designed to produce critical superstring at N=infinity, we can then expect only approximate Lorentz invariance at finite N, with violations of order 1/N^2.