Field Theory of Open and Closed Strings with Discrete Target Space

TL;DR

This paper develops a string field theory from a lattice gauge model with a discrete target space, describing open and closed strings with interactions localized at boundaries and decaying into the bulk.

Contribution

It introduces a novel quasiclassical string field theory framework based on a $U(N)$-invariant vector+matrix chain with a discrete target space, capturing topology-changing interactions.

Findings

Closed string interaction occurs only at the boundary.

Open string interaction decays exponentially with the extra dimension.

The model describes massless scalar fields in a half-space setting.

Abstract

We study a $U(N)$-invariant vector+matrix chain with the color structure of a lattice gauge theory with quarks and interpret it as a theory of open andclosed strings with target space $\Z$. The string field theory is constructed as a quasiclassical expansion for the Wilson loops and lines in this model. In a particular parametrization this is a theory of two scalar massless fields defined in the half-space $\{x\in \Z , \tau >0\} $. The extra dimension $\tau$ is related to the longitudinal mode of the strings. The topology-changing string interactions are described by a local potential. The closed string interaction is nonzero only at boundary $\tau =0$ while the open string interaction falls exponentially with $\tau$.