The purpose of this article is to extend the light-cone 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 multiloop 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.

• Received 25 May 2010

DOI:https://doi.org/10.1103/PhysRevD.82.065009