Solving Witten's SFT by Insertion of Operators on Projectors

TL;DR

This paper constructs and analyzes solutions in open string field theory by inserting operators on projectors, revealing universal energy ratios and limitations for twist invariant projectors, with applications to specific states.

Contribution

It introduces a method to solve Witten's SFT using operator insertions on projectors and derives universal energy relationships, including next-to-leading order solutions.

Findings

Energy density can reach at most 68.46% of D25-brane tension.

A universal relationship between energy density and kinetic/cubic terms is established.

Next-to-leading order solutions are constructed for regulated sliver states.

Abstract

Following Okawa, we insert operators at the boundary of regulated star algebra projectors to construct the leading order tachyon vacuum solution of open string field theory. We also calculate the energy density of the solution and the ratio between the kinetic and the cubic terms. A universal relationship between these two quantities is found. We show that for any twist invariant projector, the energy density can account for at most 68.46% of the D25-brane tension. The general results are then applied to regulated slivers and butterflies, and the next-to-leading order solution for regulated sliver states is constructed.