A solution to the 4-tachyon off-shell amplitude in cubic string field theory

TL;DR

This paper derives an exact analytic series solution for the 4-tachyon off-shell amplitude in cubic string field theory, enabling precise computation of the quartic tachyon coupling and validating previous results through convergence and agreement.

Contribution

It provides the first exact series solution for the 4-tachyon off-shell amplitude in CSFT, improving the accuracy of off-shell calculations and confirming previous numerical findings.

Findings

Exact series solution for 4-tachyon off-shell amplitude

Convergence of level-truncation coefficients to exact values

Excellent agreement with previous quartic tachyon coupling results

Abstract

We derive an analytic series solution of the elliptic equations providing the 4-tachyon off-shell amplitude in cubic string field theory (CSFT). From such a solution we compute the exact coefficient of the quartic effective action relevant for time dependent solutions and we derive the exact coefficient of the quartic tachyon coupling. The rolling tachyon solution expressed as a series of exponentials $e^t$ is studied both using level-truncation computations and the exact 4-tachyon amplitude. The results for the level truncated coefficients are shown to converge to those derived using the exact string amplitude. The agreement with previous work on the subject, both on the quartic tachyon coupling and on the CSFT rolling tachyon, is an excellent test for the accuracy of our off-shell solution.