Analytic Solutions for Tachyon Condensation with General Projectors

TL;DR

This paper develops analytic solutions for tachyon condensation in string field theory using reparameterizations of projectors, enabling explicit calculations and exploring implications for vacuum string field theory.

Contribution

It introduces a method to construct analytic solutions for arbitrary projectors in string field theory, extending the known solutions based on wedge states.

Findings

Solutions simplify for special projectors like the sliver and butterfly.

Reparameterizations enable explicit calculations in the level expansion.

Deformations of solutions can be described as operator insertions on projectors.

Abstract

The tachyon vacuum solution of Schnabl is based on the wedge states, which close under the star product and interpolate between the identity state and the sliver projector. We use reparameterizations to solve the long-standing problem of finding an analogous family of states for arbitrary projectors and to construct analytic solutions based on them. The solutions simplify for special projectors and allow explicit calculations in the level expansion. We test the solutions in detail for a one-parameter family of special projectors that includes the sliver and the butterfly. Reparameterizations further allow a one-parameter deformation of the solution for a given projector, and in a certain limit the solution takes the form of an operator insertion on the projector. We discuss implications of our work for vacuum string field theory.