We show that the scattering amplitude of four open string scalars or tachyons on the world-volume of a Dp-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 α 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 −( √ πT /α) 2 with α = 1 for bosonic theory and α = √ 2 for superstring theory.

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