Unstoppable brane-flux decay of $\overline{\text{D6}}$ branes

TL;DR

This paper demonstrates that anti-D6 branes in a flux background are inherently unstable and decay immediately due to flux singularities, challenging previous assumptions of metastability in such configurations.

Contribution

It provides the first explicit supergravity analysis showing the unavoidable decay of anti-D6 branes, highlighting the role of flux singularities and contrasting with anti-D3 brane behavior.

Findings

Anti-D6 branes decay immediately in supergravity regime.

Flux singularity at string scale causes instability.

No regular finite-temperature solutions found.

Abstract

We investigate $p$ $\overline{\text{D6}}$ branes inside a flux throat that carries $K \times M$ D6 charges with $K$ the 3-form flux quantum and $M$ the Romans mass. We find that within the calculable supergravity regime where $g_s p$ is large, the $\overline{\text{D6}}$ branes annihilate immediately against the fluxes despite the existence of a metastable state at small $p/M$ in the probe approximation. The crucial property that causes this naive conflict with effective field theory is a singularity in the 3-form flux, which we cut off at string scale. Our result explains the absence of regular solutions at finite temperature and suggests there should be a smooth time-dependent solution. We also discuss the qualitative differences between $\overline{\text{D6}}$ branes and $\overline{\text{D3}}$ branes, which makes it a priori not obvious to conclude the same instability for $\overline{\text{D3}}$ branes.