Solving Witten's SFT by Insertion of Operators on Projectors

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 nextto-leading order solution for regulated sliver states is constructed.

Analytic solution for tachyon condensation in open string field theory

“…Exact solutions were sought in the pure-gauge-like or partial-isometry form advocated in [35], but so far all such explicit solutions [36][37][38] contained the identity state of the string field algebra with some insertions and turned out to be singular. There was another class of papers [39][40][41], which attempted to find systematic analytic approximations to the exact solutions. Unfortunately, none of the above papers succeeded in proving Sen's conjectures perhaps with the exception of the third conjecture [42][43][44].…”

Comments on Schnabl's analytic solution for tachyon condensation in Witten's open string field theory

“…It solves the equation of motion when contracted with any state in the Fock space, but it does not satisfy the equation when contracted with the solution itself [25], which indicates that the assumption of the matter-ghost factorization in vacuum string field theory needs to be reconsidered [26]. While a systematic approach to accomplish the compatibility of (1.6) and (1.15) has been developed in [27,28,26], it relies on a series expansion and the compatibility is only approximate. It is therefore crucially important whether or not Schnabl's solution satisfies (1.15).…”

On surface states and star-subalgebras in string field theory

“…However, for the higher H n neither do we know of a simple algebraic description of the multiplication rule (due to the complexity of the Schwarz-Christoffel parametric problem and the lack of a simple κ-representation), nor do we know for which problem it can be of help. It is not even clear if surface states, or simple generalizations thereof such as surface states with some ghost insertions [14,46,47,48], are large enough for the problem of finding analytic string field theory solutions.…”