Stable String Bit Models

Abstract

In string bit models, the superstring emerges as a very long chain of "bits", in which s fermionic degrees of freedom contribute positively to the ground state energy in a way to exactly cancel the destabilizing negative contributions of d=s bosonic degrees of freedom. We propose that the physics of string formation be studied nonperturbatively in the class of string bit models in which s>d, so that a long chain is stable, in contrast to the marginally stable (s=d=8) superstring chain. We focus on the simplest of these models with s=1 and d=0, in which the string bits live in zero space dimensions. The string bit creation operators are N X N matrices. We choose a Hamiltonian such that the large N limit produces string moving in one space dimension, with excitations corresponding to one Grassmann lightcone worldsheet field (s=1) and no bosonic worldsheet field (d=0). We study this model at finite N to assess the role of the large N limit in the emergence of the spatial dimension. Our results suggest that string-like states with large bit number M may not exist for N<(M-1)/2. If this is correct, one can have finite chains of string bits, but not continuous string, at finite N. Only for extremely large N can such chains behave approximately like continuous string, in which case there will also be the (approximate) emergence of a new spatial dimension. In string bit models designed to produce critical superstring at N=infinity, we can then expect only approximate Lorentz invariance at finite N, with violations of order 1/N^2.

26 pages, 7 figures, error corrected in eq (81) and typos corrected

References in corpus (5)

• String Bit Models for Superstring
• Super-Galilei Invariant Field Theories in 2+1 Dimensions
• Supersymmetric Quantum Mechanics for String-Bits
• Universality and Clustering in 1+1 Dimensional Superstring-Bit Models
• The Size of a Polymer of String-Bits: A Numerical Investigation

Cited by in corpus (10)

• Space from String Bits
• String Bits at Finite Temperature and the Hagedorn Phase
• Numerical Study of the Simplest String Bit Model
• 1/N Perturbations in Superstring Bit Models
• Hagedorn Temperature in Superstring Bits and SU(N) Characters
• Color Characters for White Hot String Bits
• 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