Analytic solution for tachyon condensation in open string field theory

TL;DR

This paper introduces a new basis in open string field theory that simplifies calculations, leading to an exact analytic solution for tachyon condensation, confirming Sen's conjecture through explicit energy computations.

Contribution

A novel basis and analytic solution for tachyon condensation in open string field theory, providing a regular form and confirming theoretical predictions.

Findings

Exact analytic solution for tachyon vacuum

Simplified star product in new basis

Analytical proof of Sen's conjecture

Abstract

We propose a new basis in Witten's open string field theory, in which the star product simplifies considerably. For a convenient choice of gauge the classical string field equation of motion yields straightforwardly an exact analytic solution that represents the nonperturbative tachyon vacuum. The solution is given in terms of Bernoulli numbers and the equation of motion can be viewed as novel Euler--Ramanujan-type identity. It turns out that the solution is the Euler--Maclaurin asymptotic expansion of a sum over wedge states with certain insertions. This new form is fully regular from the point of view of level truncation. By computing the energy difference between the perturbative and nonperturbative vacua, we prove analytically Sen's first conjecture.