The Identity String Field and the Tachyon Vacuum

TL;DR

This paper demonstrates that the trivial cohomology at the tachyon vacuum is equivalent to the identity element being Q-exact, supporting Sen's conjecture and providing new computational insights in string field theory.

Contribution

It establishes a novel equivalence between cohomology triviality and the Q-exactness of the identity, using level truncation up to level nine.

Findings

Identity becomes more Q-exact as level increases

Achieved 3% accuracy at level nine

Derived a new simple expression for the identity I

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.