A Note on the Tachyon State in Vacuum String Field Theory

We re-examine the recent proposal of Rastelli, Sen and Zwiebach on the tachyon fluctuation of the vacuum string field theory representing a D25 brane, originally considered by Hata and Kawano. We show that the tachyon state satisfies the linearized equations of motion on-shell in the strong sense thereby allowing us to calculate the ratio Ec T25 of energy density to the tension of the D-brane to be Ec T25 ≃ π 3 1 16(ln2)3 ≃ 0.62. Our proof relies on a careful handling of the limits (n → ∞) involved in the conformal theory description of the sliver and tachyon states. We conjecture that the sliver state represents a single D25 brane. e-mails: [email protected]; [email protected], on leave of absence from Dept. of Physics, Sofia University, 1164 Sofia, Bulgaria e-mail: [email protected]