Slowly varying tachyon and tachyon potential

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 ${\alpha }^{\prime }$ 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.

Latex, 11 pages, no figures v3; clarify that the potential found is only the even part of the tachyon potential

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