A Note on a Proposal for the Tachyon State in Vacuum String Field Theory

TL;DR

This paper analyzes a proposed tachyon fluctuation in vacuum string field theory, providing a conformal field theory construction and discussing the mismatch in D-brane tension calculations.

Contribution

It offers a conformal field theory construction of the tachyon state and explains the reasons for tension calculation discrepancies in vacuum string field theory.

Findings

Conformal field theory construction of the tachyon state

Correct emergence of the on-shell momentum condition

Identification of issues with tension computation due to equations of motion

Abstract

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 $(\pi^2/3)(16/27\ln 2)^3 \simeq 2.0558$ 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.