On D-brane-Anti D-brane Effective actions and their all order Bulk Singularity Structures

TL;DR

This paper computes all-order string amplitude corrections for brane-antibrane systems, revealing bulk singularity structures and fixing vertex operators, thereby advancing the understanding of their effective actions.

Contribution

It provides the first comprehensive all-order $ ext{alpha'}$ corrections for four- and five-point functions involving brane-antibrane systems, including vertex operator fixes and singularity structures.

Findings

Identified two types of bulk singularity structures involving infinite gauge and scalar poles.

Fixed the vertex operator of RR in asymmetric picture and confirmed picture independence.

Derived effective couplings with all-order $ ext{alpha'}$ corrections for brane-antibrane interactions.

Abstract

All four point functions of brane anti brane system including their correct all order $\alpha'$ corrections have been addressed. All five point functions of one closed string Ramond-Ramond (RR), two real tachyons and either one gauge field or the scalar field in both symmetric and asymmetric pictures have also been explored. The entire analysis of $<C^{-2} A^0 T^0 T ^{0}>$ is carried out. Not only does it fix the vertex operator of RR in asymmetric picture and in higher point functions of string theory amplitudes but also it confirms the fact that there is no issue of picture dependence of the mixed closed RR, gauge fields, tachyons and fermion fields in all symmetric or anti symmetric ones. We compute $<C^{-2} \phi^0 T^0 T ^{0}>$ S-matrix in the presence of a transverse scalar field, two real tachyons and that reveals two different kinds of bulk singularity structures, involving an infinite number of $u$- channel gauge field and $(u+s'+t')$- channel scalar bulk poles. In order to produce all those bulk singularity structures, we define various couplings at the level of the effective field theory that involve the mixing term of Chern-Simons coupling (with C-potential field) and a covariant derivative of the scalar field that comes from the pull-back of brane. Eventually we explore their all order $\alpha'$ corrections in the presence of brane anti brane system where various remarks will be also pointed out.