Space from String Bits

TL;DR

This paper develops superstring bit models replacing transverse coordinates with flavor indices, analyzing the emergence of string coordinates from spin chain dynamics in the large N limit, with implications for string stability.

Contribution

Introduces a superstring bit model where transverse coordinates emerge from flavor fluctuations modeled by anisotropic Heisenberg spin chains, connecting spin chain physics to string theory.

Findings

String coordinates emerge from flavor fluctuations in spin chains.

Low energy excitations match string worldsheet modes.

Stability depends on the relation between d and s, with d=s=8 being marginally stable.

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.)