Slowly varying tachyon and tachyon potential

TL;DR

This paper derives a universal form for the scattering amplitude of open string scalars or tachyons on D-branes in bosonic string theory, revealing a consistent tachyonic DBI action with a specific potential form.

Contribution

It presents a universal expression for four-point open string amplitudes and connects it to a specific tachyon potential in the DBI action for both bosonic and superstring theories.

Findings

Amplitude matches a universal form with an extra tachyonic pole in bosonic theory.

Tachyon potential in the DBI action is exponential with a quadratic argument.

Results are consistent with slowly varying fields and $ ext{alpha'}$ expansion.

Abstract

We show that the scattering amplitude of four open string scalars or tachyons on the world-volume of a D$_p$-brane in the bosonic string theory can be written in a universal form. The difference between this amplitude and the corresponding amplitude in the superstring theory is in an extra tachyonic pole. We show that in an $\alpha'$ expansion and for slowly varying fields, the amplitude is consistent with the tachyonic DBI action in which the even part of the tachyon potential is $V(T)=e^{-(\sqrt{\pi} T/\alpha)^2}$ with $\alpha=1$ for bosonic theory and $\alpha=\sqrt{2}$ for superstring theory.