Analytical Solutions of Open String Field Theory

TL;DR

This paper reviews analytical solutions in open string field theory, focusing on Schnabl's tachyon vacuum solution, its representations, proofs of Sen's conjectures, and extensions to superstring theories.

Contribution

It provides a comprehensive survey of analytical solutions in open string field theory, including geometric, algebraic, and oscillator representations, and discusses their extensions to superstring theories.

Findings

Analytical proofs of Sen's conjectures for the tachyon vacuum.

Various representations of the tachyon vacuum solution.

Extension of solutions to superstring field theory without tachyons.

Abstract

In this work we review Schnabl's construction of the tachyon vacuum solution to bosonic covariant open string field theory and the results that followed. We survey the state of the art of string field theory research preceding this construction focusing on Sen's conjectures and the results obtained using level truncation methods. The tachyon vacuum solution can be described in various ways. We describe its geometric representation using wedge states, its formal algebraic representation as a pure-gauge solution and its oscillator representation. We also describe the analytical proofs of some of Sen's conjectures for this solution. The tools used in the context of the vacuum solution can be adapted to the construction of other solutions, namely various marginal deformations. We present some of the approaches used in the construction of these solutions. The generalization of these ideas to open superstring field theory is explained in detail. We start from the exposition of the problems one faces in the construction of superstring field theory. We then present the cubic and the non-polynomial versions of superstring field theory and discuss a proposal suggesting their classical equivalence. Finally, the bosonic solutions are generalized to this case. In particular, we focus on the (somewhat surprising) generalization of the tachyon solution to the case of a theory with no tachyons.