1/N Perturbations in Superstring Bit Models

TL;DR

This paper develops a 1/N expansion for superstring bit models, revealing a novel 'protostring' with 24 Grassmann dimensions that could connect to superstring theory.

Contribution

It introduces a new string bit model with a 1/N expansion, leading to the discovery of a 'protostring' with unique properties and potential links to superstring theory.

Findings

At leading order, models produce a discretized lightcone string.

Higher orders determined by overlaps of chains without operator insertions.

Critical Grassmann dimension s=24 leads to the protostring with no tachyons or massless particles.

Abstract

We develop the 1/N expansion for stable string bit models, focusing on a model with bit creation operators carrying only transverse spinor indices a=1,...,s. At leading order (1/N=0), this model produces a (discretized) lightcone string with a "transverse space' of $s$ Grassmann worldsheet fields. Higher orders in the 1/N expansion are shown to be determined by the overlap of a single large closed chain (discretized string) with two smaller closed chains. In the models studied here, the overlap is not accompanied with operator insertions at the break/join point. Then the requirement that the discretized overlap have a smooth continuum limit leads to the critical Grassmann "dimension" of s=24. This "protostring", a Grassmann analog of the bosonic string, is unusual, because it has no large transverse dimensions. It is a string moving in one space dimension and there are neither tachyons nor massless particles. The protostring, derived from our pure spinor string bit model, has 24 Grassmann dimensions, 16 of which could be bosonized to form 8 compactified bosonic dimensions, leaving 8 Grassmann dimensions--the worldsheet content of the superstring. If the transverse space of the protostring could be "decompactified", string bit models might provide an appealing and solid foundation for superstring theory.