Improved Off-Shell Scattering Amplitudes in String Field Theory and New Computational Methods

TL;DR

This paper advances the computation of off-shell scattering amplitudes in Witten's cubic string field theory by completing the derivation of the Veneziano formula within the Moyal star formulation, demonstrating agreement with other methods, and developing new computational techniques.

Contribution

It introduces new explicit results for off-shell amplitudes, extends computational methods in MSFT, and highlights the importance of the SL(2,R) representation in practical calculations.

Findings

Explicit off-shell 4-tachyon amplitude results obtained.

Demonstrated agreement between MSFT and other approaches.

Developed techniques applicable to nonperturbative processes.

Abstract

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 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 representation of SL(2,R) generated by the Virasoro operators $L_{0},L_{\pm1}$ 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.