Space from string bits

Charles B. Thorn
2014 Journal of High Energy Physics  
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->∞, in which closed chains of many string bits behave like free lightcone IIB superstrings with d compact coordinate bosonic worldsheet fields
more » ... x^k, and s pairs of Grassmann fermionic fields θ_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<Δ_k<1 of the corresponding Heisenberg system. Furthermore there is a limit of this parameter, Δ_k->± 1, in which R_k->∞. As noted in earlier work [Phys.Rev.D 89(2014)105002], these multi-string-bit chains are strictly stable at N=∞ 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.)
doi:10.1007/jhep11(2014)110 fatcat:s43ctwg6tvhzdlxfbytvguwnry