A note on the 3D Ising model as a string theory

TL;DR

This paper reformulates the lattice theory of surfaces related to the 3D Ising model to make the continuum limit more straightforward, supporting its interpretation as a string theory.

Contribution

It introduces a new formulation of the lattice surface theory that simplifies taking the continuum limit, addressing previous obstacles in relating the 3D Ising model to string theory.

Findings

New lattice formulation facilitates continuum limit

Addresses objections to Ising-string equivalence

Discusses fermion doubling in related models

Abstract

It has long been argued that the continuum limit of the 3D Ising model is equivalent to a string theory. Unfortunately, in the usual starting point for this equivalence -- a certain lattice theory of surfaces -- it is not at all obvious how to take the continuum limit. In this note, I reformulate the lattice theory of surfaces in a fashion such that the continuum limit is straightforward. I go on to discuss how this new formulation may overcome some fundamental objections to the notion that the Ising model is equivalent to a string theory. In an appendix, I also discuss some aspects of fermion doubling, and the lattice fermion formulation of the 2D Ising model.