A Vacuum Loop of an Open String around an Identity-Based Solution

Abstract

Bosonic Open String field theory has classical solutions describing a tachyon vacuum where D-branes completely annihilate. First, a numerical solution was constructed by using level truncation approximation in the Siegel gauge.1),2) Then, analytic classical solutions were constructed in terms of an identity string field∗) or wedge-like states.4) Although there are some differences, it is thought that these types of solutions possess certain properties of the tachyon vacuum: its vacuum energy density cancels a D-brane tension and the kinetic operator on its vacuum has vanishing cohomology.6),7) This makes us believe that these solutions correspond to the tachyon vacuum, but an important problem remains unsolved. How can we find closed strings on the vacuum? It has been noted that the identity-based solution provides the possibility of understanding closed strings on the vacuum. In the theory expanded around the identity-based solution, we can construct a Siegel gauge propagator acting on the usual open string Fock space. As pointed out by Drukker, the propagator generates a worldsheet swept by an open string, but the boundary is fixed at a point in the case of the tachyon vacuum solution.8) Hence, an amplitude calculated by the propagator corresponds to a worldsheet without boundaries, that is a closed string surface generated by closed strings. This closed worldsheet picture around the identity-based solution provides fascinating possibility to find closed strings of the tachyon vacuum. However, we encounter divergence difficulties if we calculate the amplitude explicitly. In this talk, we regularize this divergent amplitude by using level truncation approximation in order to explore the possibility of finding closed strings of the tachyon vacuum. In §2, we will give a brief review on the identity-based solution. In §3, we will provide a vacuum loop amplitude of an open string in the expanded theory. Finally, we will give concluding remarks in §4. This talk is based on the work in collaboration with S. Inatomi, I. Kishimoto and Y. Saito.