(Anti-)Brane backreaction beyond perturbation theory

TL;DR

This paper investigates the full backreaction of anti-D6-branes in a flux background, demonstrating that only solutions with certain boundary conditions are consistent, and identifying a singular but integrable flux energy density.

Contribution

It provides a non-perturbative analysis of anti-D6-brane backreaction, avoiding smearing and perturbative assumptions, and clarifies boundary conditions for consistent solutions.

Findings

Only two boundary conditions are consistent with the equations of motion.

Regular H flux boundary condition is eliminated by a topological argument.

The remaining boundary condition involves a singular but integrable flux energy density.

Abstract

We improve on the understanding of the backreaction of anti-D6-branes in a flux background that is mutually BPS with D6-branes. This setup is analogous to the study of the backreaction of anti-D3-branes inserted in the KS throat, but does not require us to smear the anti-branes or do a perturbative analysis around the BPS background. We solve the full equations of motion near the anti-D6-branes and show that only two boundary conditions are consistent with the equations of motion. Upon invoking a topological argument we eliminate the boundary condition with regular H flux since it cannot lead to a solution that approaches the right kind of flux away from the anti-D6-brane. This leaves us with a boundary condition which has singular, but integrable, H flux energy density.