Stable string bit models
Songge Sun, Charles B. Thorn · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · 2014
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 $N\ifmmode\times\else\texttimes\fi{}N$ matrices. We choose a Hamiltonian such that the large $N$ limit produces a string moving in one space dimension, with excitations corresponding to one Grassmann light-cone world sheet field ($s=1$) and no bosonic world sheet 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 stringlike states with large bit number $M$ may not exist for $N\ensuremath{\le}(M\ensuremath{-}1)/2$. If this is correct, one can have finite chains of string bits, but not a continuous string, at finite $N$. Only for extremely large $N$ can such chains behave approximately like a continuous string, in which case there will also be the (approximate) emergence of a new spatial dimension. In string bit models designed to produce a critical superstring at $N=\ensuremath{\infty}$, we can then expect only approximate Lorentz invariance at finite $N$, with violations of order $1/{N}^{2}$.