On-shell S-matrix and tachyonic effective actions

TL;DR

This paper computes disk-level four-point functions involving scalars and tachyons in superstring theory with background B-flux, deriving couplings consistent with non-commutative tachyonic DBI action and fixing the tachyon potential coefficient.

Contribution

It provides explicit string amplitude calculations that determine couplings and coefficients in the non-commutative tachyonic effective action for non-BPS D-branes.

Findings

Derived couplings of two scalars with two tachyons.

Obtained couplings of four tachyons.

Fixed the coefficient of the $T^4$ term in the tachyon potential.

Abstract

We evaluate various disk level four-point functions involving the massless scalar and tachyon vertex operators in the presence of background B-flux in superstring theory. By studying these amplitudes in specific limits, we find couplings of two scalars with two tachyons, and couplings of four tachyons on the world-volume of non-BPS D-branes of superstring theory. They are fully consistent with the non-commutative tachyonic Dirac-Born-Infeld effective action. They also fix the coefficient of $T^4$ term in the expansion of the tachyon potential around its maximum.