We report on new results in Witten’s cubic string field theory for the off-shell factor in the 4-tachyon amplitude that was not fully obtained explicitly before. This is achieved by completing the derivation of the Veneziano formula in the Moyal star formulation of Witten’s string field theory (MSFT). We also demonstrate a detailed agreement of MSFT with a number of on-shell and off-shell computations in other approaches to Witten’s string field theory. We extend the techniques of computation in MSFT, and show that the $j=0\mathrm{}$ representation of $\mathrm{SL}\mathrm{}(2,R)\mathrm{}$ generated by the Virasoro operators $L_0{,L}_{\pm 1}$ is a key structure in practical computations for generating numbers. We provide more insight into the Moyal structure that simplifies string field theory, and develop techniques that could be applied more generally, including nonperturbative processes.

• Received 9 December 2003

DOI:https://doi.org/10.1103/PhysRevD.69.086007