Continuous Half-String Representation of String Field Theory

TL;DR

This paper develops an explicit continuous half-string representation in string field theory, clarifying the structure of vertices and ghost sectors, and demonstrating its utility through applications like gauge transformations.

Contribution

It introduces a novel continuous half-string formalism, detailing the vertex structure and ghost sector treatment, enhancing the analytical tools in string field theory.

Findings

Explicit form of the half-string representation in the continuous kappa basis.

Demonstration of the comma structure of the three-vertex.

Application to gauge transformations and subalgebra identification.

Abstract

We give the explicit form of the half-string representation in the continuous kappa basis. We show the comma structure of the three-vertex, when expanded around an arbitrary projector, and that the zero-mode must be replaced by the mid-point degree of freedom in the half-string representation. The treatment of the ghost sector enables us to calculate the normalization of the vertices. The simplicity of this formalism is demonstrated with some applications, such as gauge transformations and identification of subalgebras.