A note on a proposal for the tachyon state in vacuum string field theory

We discuss the proposal of Hata and Kawano for the tachyon fluctuation around a solution of vacuum string field theory representing a D25-brane. We give a conformal field theory construction of their state - a local insertion of a tachyon vertex operator on the sliver surface state, and explain why the on-shell momentum condition emerges correctly. We also show that a naive computation of the D25-brane tension using data for the three point coupling of this state gives an answer that is (π²/3) (16/27 ln 2)³ ≃ 2.0558 times the expected answer. We demonstrate that this problem arises because the HK state does not satisfy the equations of motion in a strong sense required for the computation of D-brane tension from the on-shell 3-tachyon coupling.