Schnabl's Solution Research Articles

Cubic interaction term for Schnabl's solution using Padé approximants

We evaluate the cubic interaction term in the action of open bosonic string field theory for Schnabl's solution written in terms of Bernoulli numbers. This computation provides us with new evidence for the fact that the string field equation of motion is satisfied when it is contracted with the solution itself.

Schnabl's solution and boundary states in open string field theory

We discuss that Schnabl's solution is an off-shell extension of the boundary state describing a D-brane in the closed string sector. It gives the physical meaning of the gauge-invariant overlaps for the solution in our previous paper and supports Ellwood's recent proposal in the operator formalism.

Gauge invariant overlaps for classical solutions in open string field theory

We calculate gauge invariant observables for Schnabl's solution with analytic method and with the level truncation approximation. We also compute them for the numerical solution initially obtained by Sen and Zwiebach in the level truncation approximation to compare with the one for Schnabl's solution. The results are consistent with the expectation that they may be gauge equivalent. We briefly discuss the gauge invariant observables and the action for a marginal solution with a nonsingular current.

Level truncation analysis of exact solutions in open string field theory

We evaluate vacuum energy density of Schnabl's solution using the level truncation calculation and the total action including interaction terms. The level truncated solution provides vacuum energy density expected both for tachyon vacuum and trivial pure gauge. We discuss the role of the phantom term to reproduce correct vacuum energy.

Ghost story. I. Wedge states in the oscillator formalism

This paper is primarily devoted to the ghost wedge states in string field theory formulated with the oscillator formalism. Our aim is to prove, using such formalism, that the wedge states can be expressed as |n = exp{[(2−n)/2](0+0†)}|0, separately in the matter and ghost sector. This relation is crucial for instance in the proof of Schnabl's solution. We start from the exponentials in the rhs and wish to prove that they take precisely the form of wedge states. As a guideline we first re-demonstrate this relation for the matter part. Then we turn to the ghosts. On the way we face the problem of `diagonalizing' infinite rectangular matrices. We manage to give a meaning to such an operation and to prove that the eigenvalues we obtain satisfy the recursion relations of the wedge states.

Split string formalism and the closed string vacuum, II

In this paper we consider a class of generalizations of Schnabl's solution of open bosonic string field theory obtained by replacing the wedge state by an arbitrary combination of wedge states. We find that under a few modest conditions such generalizations give a sensible deformation of Schnabl's solution for the closed string vacuum--in particular, we can compute their energies and show that they reproduce the value predicted by Sen's conjecture. Though these solutions are apparently gauge equivalent, they are not in general related by midpoint-preserving reparameterizations.

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

Schnabl recently constructed an analytic solution for tachyon condensation in Witten's open string field theory. The solution consists of two pieces. Only the first piece is involved in proving that the solution satisfies the equation of motion when contracted with any state in the Fock space. On the other hand, both pieces contribute in evaluating the kinetic term to reproduce the value predicted by Sen's conjecture. We therefore need to understand why the second piece is necessary. We evaluate the cubic term of the string field theory action for Schnabl's solution and use it to show that the second piece is necessary for the equation of motion contracted with the solution itself to be satisfied. We also present the solution in various forms including a pure-gauge configuration and provide simpler proofs that it satisfies the equation of motion.