Digitizing the Neveu-Schwarz Model on the Lightcone Worldsheet

TL;DR

This paper extends the lightcone worldsheet lattice framework to include the Neveu-Schwarz string model by modeling fermionic fields with Ising models, enabling potential numerical computations in string theory and large N QCD.

Contribution

It introduces a lattice representation of the Neveu-Schwarz model using Ising models for fermions, including boundary conditions, G-parity projection, and vertex construction.

Findings

Successful modeling of fermionic fields with Ising models.

Formulation of the open string vertex on the lattice.

Discussion of summing multi-loop amplitudes numerically.

Abstract

The purpose of this article is to extend the lightcone worldsheet lattice description of string theory to include the Neveu-Schwarz model. We model each component of the fermionic worldsheet field by a critical Ising model. We show that a simple choice of boundary conditions for the Ising variables leads to the half integer modes required by the model. We identify the G-parity operation within the Ising model and formulate the procedure for projecting onto the even G-parity sector. We construct the lattice version of the three open string vertex, with the necessary operator insertion at the interaction point. We sketch a formalism for summing planar open string multi-loop amplitudes, and we discuss prospects for numerically summing them. If successful, the methods described here could provide an alternative to lattice gauge theory for computations in large N QCD.