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

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.Comment: 21 pages, 11 figures. This revised manuscript is identical to the final published version (Nuclear Physics B, to appear). Aside from correcting some scattered typos, the final version corrects and expands some of the comments in the original preprint on the unoriented NSR strin