Numerical Study of the Simplest String Bit Model

Abstract

String bit models provide a possible method to formulate a string as a discrete chain of pointlike string bits. When the bit number $M$ is large, a chain behaves as a continuous string. We study the simplest case that has only one bosonic bit and one fermionic bit. The creation and annihilation operators are adjoint representations of the $U\left(N\right)$ color group. We show that the supersymmetry reduces the parameter number of a Hamiltonian from 7 to 3 and, at $N=\infty$, ensures a continuous energy spectrum, which implies the emergence of one spatial dimension. The Hamiltonian $H_0$ is constructed so that in the large $N$ limit it produces a world sheet spectrum with one Grassmann world sheet field. We concentrate on numerical study of the model in finite $N$. For the Hamiltonian $H_0$, we find that the would-be ground energy states disappear at $N=\left(M-1\right)/2$ for odd $M\le 11$. Such a simple pattern is spoiled if $H$ has an additional term $\xi \Delta H$ which does not affect the result of $N=\infty$. The disappearance point moves to higher (lower) $N$ when $\xi$ increases (decreases). Particularly, the $\pm \left(H_0-\Delta H\right)$ cases suggest a possibility that the ground state could survive at large $M$ and $M\gg N$. Our study reveals that the model has stringy behavior: when $N$ is fixed and large enough, the ground energy decreases linearly with respect to $M$, and the excitation energy is roughly of order $M^{-1}$. We also verify that a stable system of Hamiltonian $\pm H_0+\xi \Delta H$ requires $\xi \ge \mp 1$.

arXiv comment54 pages, 15 figures

References in corpus (5)

• Dimensional Reduction in Quantum Gravity
• Reformulating String Theory with the $1/N$ Expansion
• String Bit Models for Superstring
• Stable String Bit Models
• 1/N Perturbations in Superstring Bit Models

Cited by in corpus (7)

• Hagedorn Temperature in Superstring Bits and SU(N) Characters
• Color Characters for White Hot String Bits
• Thermal properties of a string bit model at large N
• Protostring Scattering Amplitudes
• Cubic Interaction Vertices and One-loop Self-energy in the Stable String Bit Model
• Heisenberg spin chain as a worldsheet coordinate for lightcone quantized string
• Internal and Super Symmetry in String Bit Models