The Identity String Field and the Tachyon Vacuum

TL;DR

This paper reduces the problem of open-string decoupling at the tachyon vacuum to the exactness of the identity in the star-algebra by seeking a ghost-number -1 state A such that the new BRST operator Q_Psi0 satisfies Q_Psi0 A = I. Using level truncation up to level 9, the authors construct A (in two gauge choices) with approximately 3% accuracy, providing strong evidence that the cohomology of Q_Psi0 is trivial and hence that all open-string degrees of freedom disappear around the tachyon vacuum. They also derive a new analytic expression for the identity and discuss the interpretation of the identity as an approximate unit in the OSFT star algebra, highlighting slow convergence due to anomalies and proposing avenues for analytic progress and gauge choices. The results reinforce a strong version of Sen's conjecture and offer a practical computational framework for exploring the vacuum structure of open string field theory and its relation to closed-string dynamics.

Abstract

We show that the triviality of the entire cohomology of the new BRST operator Q around the tachyon vacuum is equivalent to the Q-exactness of the identity I of the star-algebra. We use level truncation to show that as the level is increased, the identity becomes more accurately Q-exact. We carry our computations up to level nine, where an accuracy of 3% is attained. Our work supports, under a new light, Sen's conjecture concerning the absence of open string degrees of freedom around the tachyon vacuum. As a by-product, a new and simple expression for I in terms of Virasoro operators is found.

Figures (1)

• Figure 1: A plot of $q_{0,1}(\ell)$ (solid curve), $q_{2,1}(\ell)$ (dotted curve) and $q_{2,3} (\ell)$ (dashed curve) as functions of the level $\ell$ of the identity. $\ell$ goes from $3$ to $17$.