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 (π/3)(16/27 ln 2) ≃ 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.