Space from String Bits

Abstract

We develop superstring bit models, in which the lightcone transverse coordinates in D spacetime dimensions are replaced with d=D-2 double-valued "flavor" indices $x^k-> f_k=1,2$; $k=2,...,d+1$. In such models the string bits have no space to move. Letting each string bit be an adjoint of a "color" group U(N), we then analyze the physics of 't Hooft's limit $N->\infty$, in which closed chains of many string bits behave like free lightcone IIB superstrings with d compact coordinate bosonic worldsheet fields $x^k$, and s pairs of Grassmann fermionic fields $\theta_{L,R}^a$, a=1,..., s. The coordinates $x^k$ emerge because, on the long chains, flavor fluctuations enjoy the dynamics of d anisotropic Heisenberg spin chains. It is well-known that the low energy excitations of a many-spin Heisenberg chain are identical to those of a string worldsheet coordinate compactified on a circle of radius $R_k$, which is related to the anisotropy parameter $-1<\Delta_k<1$ of the corresponding Heisenberg system. Furthermore there is a limit of this parameter, $\Delta_k->\pm 1$, in which $R_k->\infty$. As noted in earlier work [Phys.Rev.D{\bf 89}(2014)105002], these multi-string-bit chains are strictly stable at $N=\infty$ when d<s and only marginally stable when d=s. (Poincare supersymmetry requires d=s=8, which is on the boundary between stability and instability.)