On gravitational couplings in D-brane action
A. Fotopoulos, A.A. Tseytlin

TL;DR
This paper calculates a specific scattering amplitude in string theory to demonstrate the absence of a particular curvature-scalar coupling term in the low-energy effective action of D-branes in curved space.
Contribution
It provides a direct string-theoretic computation confirming the non-existence of the R X^2 coupling in the D-brane effective action.
Findings
No second-derivative curvature-scalar coupling term R X^2 found
Supports the consistency of the D-brane effective action in curved backgrounds
Clarifies the structure of couplings in superstring theory
Abstract
We compute the two closed string graviton - two open string scalar scattering amplitude on the disc to show that there is no second-derivative curvature - scalar coupling term R X^2 in the low-energy effective action of a D-brane in curved space in type II superstring theory.
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