On the dynamics of BMN operators of finite size and the model of string bits

TL;DR

This paper investigates discretization effects in a string-bit model for near-BMN operators, addressing species doubling issues and proposing a supersymmetric formulation that results in an even number of strings as the system size grows.

Contribution

It introduces an alternative fermionic sector formulation free from species doubling and a supersymmetric string-bit model with specific large-size behavior.

Findings

Proposed a cure for species doubling in the fermionic sector.

Developed a supersymmetric string-bit formulation with exact supersymmetry.

Achieved an even number of strings in the large J limit.

Abstract

We consider the discretization effects of a string-bit model simulating the near-BMN operators in the super--Yang--Mills model. The fermionic sector of this model is altered by the so called species doubling. We analyze the possibilities to cure this disease and propose an alternative formulation of the fermionic sector free from the above drawbacks. Also we propose a formulation of string bits with exact supersymmetry, which produces however an even number of continuous strings in the limit $J\to\infty$.