Cubic Interaction Vertices and One-loop Self-energy in the Stable String Bit Model

Abstract

We provide a formalism to calculate the cubic interaction vertices of the stable string bit model, in which string bits have $s$ spin degrees of freedom but no space to move. With the vertices, we obtain a formula for one-loop self-energy, i.e., the $\mathcal{O}\left(1/N^2\right)$ correction to the energy spectrum. A rough analysis shows that, when the bit number $M$ is large, the ground state one-loop self-energy $\Delta E_G$ scale as $M^{5-s/4}$ for even $s$ and $M^{4-s/4}$ for odd $s$. Particularly, in $s=24$, we have $\Delta E_G\sim 1/M$, which resembles the Poincaré invariant relation $P^{-}\sim 1/P^{+}$ in $(1+1)$ dimensions. We calculate analytically the one-loop correction for the ground energies with $M=3$ and $s=1,2$. We then numerically confirm that the large $M$ behavior holds for $s\le 4$ cases.

33 pages, 14 figures, update to the published version

References in corpus (4)

• Space from String Bits
• Stable String Bit Models
• Numerical Study of the Simplest String Bit Model
• 1/N Perturbations in Superstring Bit Models

Cited by in corpus (1)

• Internal and Super Symmetry in String Bit Models