Topics in String Field Theory

TL;DR

This review explores bosonic string field theory focusing on the three string vertex, Neumann coefficients, and lump solutions, including their relation to D-branes and GMS solitons, using new methods for simplification.

Contribution

It introduces a new method for deriving Neumann coefficients and provides a comprehensive analysis of lump solutions and their connection to D-branes and GMS solitons.

Findings

Derived Neumann coefficients using a conformal field theory approach.

Constructed lump solutions interpreted as D-branes.

Showed lump solutions flow toward GMS solitons in the low energy limit.

Abstract

This review of bosonic string field theory is concentrated on two main subjects. In the first part we revisit the construction of the three string vertex and rederive the relevant Neumann coefficients both for the matter and the ghost part following a conformal field theory approach. We use this formulation to solve the VSFT equation of motion for the ghost sector. This part of the paper is based on a new method which allows us to derive known results in a simpler way. In the second part we concentrate on the solution of the VSFT equation of motion for the matter part. We describe the construction of the three strings vertex in the presence of a background B field. We determine a large family of lump solutions, illustrate their interpretation as D-branes and study the low energy limit. We show that in this limit the lump solutions flow toward the so-called GMS solitons.