On higher derivative corrections of tachyon action

TL;DR

This paper derives all-order higher derivative couplings of tachyons and gauge fields on non-BPS D-branes and brane-anti-brane systems, confirming their consistency with string scattering amplitudes.

Contribution

It provides the complete set of higher derivative couplings for tachyons and gauge fields in these systems, extending previous results to all orders in '.

Findings

Exact match of massless poles between field theory and string amplitudes.

Derivation of infinite tower of couplings for tachyons and gauge fields.

Confirmation of the proposed D-brane-anti-brane action structure.

Abstract

We have examined the momentum expansion of the disk level S-matrix element of two tachyons and two gauge fields to find, up to on-shell ambiguity, the couplings of these fields in the world volume theory of N coincident non-BPS D-branes to all order of $\alpha'$. Using the proposal that the action of D-brane-anti-D-brane is given by the projection of the action of two non-BPS D-branes with $(-1)^{F_L}$, we find the corresponding couplings in the world volume theory of the brane-anti-brane system. Using these infinite tower of couplings, we then calculate the massless pole of the scattering amplitude of one RR field, two tachyons and one gauge field in the brane-anti-brane theory. We find that the massless pole of the field theory amplitude is exactly equal to the massless pole of the disk level S-matrix element of one RR, two tachyons and one gauge field to all order of $\alpha'$.