A Proposal for the Vector State in Vacuum String Field Theory

A previous calculation on the tachyon state arising as fluctuations of a $D$ brane in vacuum string field theory is extended to include the vector state. We use the boundary conformal field theory approach of Rastelli, Sen and Zwiebach to construct a vector state. It is shown that the vector field satisfies the linearized equations of motion provided the two conditions $k^2=0$ and $k^\mu A_\mu=0$ are satisfied. Earlier calculations using Fock space techniques by Hata and Kawano have found massless vector states that are not necessarily transverse.