World Sheet Geometry of Classical Solutions in String Field Theory

TL;DR

This paper explores the geometric structure of classical solutions in string field theory, revealing how the worldsheet geometry changes when certain poles of a quadratic differential coincide, affecting the string boundary.

Contribution

It demonstrates the geometric interpretation of solutions via Jenkins-Strebel differentials and identifies conditions under which the solution becomes nontrivial.

Findings

The BRS charge and propagator are described by Jenkins-Strebel differentials.

Solutions become nontrivial when two poles of the differential coincide.

Open string boundary shrinks to a point at the critical configuration.

Abstract

We investigate classical solutions of string field theory proposed by Takahashi and Tanimoto in the case of even order polynomial functions. The BRS charge and the Feynman propagator of open string field theory expanded around the solution are specified by Jenkins-Strebel quadratic differential, which describes geometry of the string worldsheet. We show that the solution becomes nontrivial when two second order poles of the quadratic differential coincide each other on the unit disk. In this case, an open string boundary shrinks to a point.