The D0$-$D8 system revisited

TL;DR

This paper revisits the D0-D8 brane system, addressing divergence issues in the interaction potential and testing interpretations with fluxes, ultimately reinforcing the understanding of D8 branes' nature.

Contribution

It improves existing interpretations of the D0-D8 system by properly handling divergences and analyzing flux effects, clarifying the system's physical consistency.

Findings

Divergences in the R-R and NS-NS sectors are properly addressed.

Fluxes on D8 branes do not resolve divergence issues.

The nature of D8 branes as independent objects is reinforced.

Abstract

We address a few subtle issues regarding the interacting D0-D8 system. There are two existing interpretations for the counter-intuitive non-vanishing cylinder-diagram R-R potential. We improve them each by properly dealing with the divergence of potential in the R-R as well as the NS-NS sector, which has been ignored so far. We further test them by considering the D8 to carry a flux, electric or magnetic. We find that the improved interpretations continue to hold. We resolve a subtle issue regarding the regularization of fermionic zero-modes in the R-R sector when the D8 carries an electric flux so that a meaningful result for the potential can be calculated. The persistence of divergence for the potential in either sector in the presence of a flux on the D8 brane indicates that adding a flux/fluxes on the D8 brane doesn't help to improve its nature of existence as an independent object, therefore reenforcing the previous assertion on D8 branes.