A note on M2-branes in opposite charge

TL;DR

This work investigates flux singularities that arise when $M2$-branes are placed in oppositely charged flux within $11$D supergravity. It constructs new smeared $AdS_3$ solutions with space-filling (anti-)M2-branes in oppositely charged flux and derives a topological obstruction that constrains flux profiles during localisation, forcing a singular flux density at the brane. The analysis is extended to include a horizon (blackening) which cannot shield the singularity, instead relocating it to the horizon surface. The results suggest that such flux singularities persist in full backreaction and challenge potential M-theory resolutions that rely on horizon cloaking.

Abstract

The flux singularity that arise when branes are put in an oppositely charged background is a wildly discussed issue and in this paper the problem is investigated further. New AdS world volume (anti-)M2-brane solutions are constructed by placing the brane in a background where the charge dissolved in the flux is opposite that of the brane. A topological obstruction is derived to show how the singularity develops during localisation of this solution and any similarly constructed solution. Furthermore the singularity is shown not to be possible to hide behind a horizon, which would have given credence to a possible M-theory resolution.

Figures (2)

• Figure 1: The curvature of the ${}^{(H)}$ section is the dashed red line and the ${}^{(F)}$ section is the dotted blue line. The full purple line is the total curvature of the internal space. The left (right) side of the vertical axis is where $Q$ is positive (negative) and $\lambda$ is negative (positive).
• Figure 2: The left sketch is excluded by (\ref{['eq:nogo']}), the middle is excluded by (\ref{['eq:bc']}), the right remains allowed and implies flux that is singular an not mutually BPS with the brane.