Antibranes don't go black

TL;DR

This work addresses whether anti-branes placed in flux backgrounds can form regular black branes or remain singular, focusing on codimension-three configurations such as anti-D6 in massive IIA and anti-D3 smeared on a $\mathbb{T}^3$ within $\mathbb{R}^3\times\mathbb{T}^3$. By analyzing the $H$-flux equation of motion and Bianchi identities, the authors derive a no-go condition: any would-be black brane with horizon charge $Q$ opposite in sign to the ambient flux necessarily yields a divergent $H$-flux at the horizon, i.e., a singular horizon. This analytic result extends via T-duality to smeared anti-$p$-branes with $p<6$, showing the same sign constraint on horizon charge and ruling out regular horizons for opposite-sign configurations. The findings reinforce the physical picture that brane-flux annihilation occurs immediately upon attempting to blacken anti-branes in positive-flux backgrounds, with potential implications for uplift scenarios and the existence of metastable vacua in string theory.

Abstract

When D-branes are inserted in flux backgrounds of opposite charge, the resulting solution has a certain singularity in the fluxes. Recently it has been argued, using numerical solutions, that for anti-D3 branes in the Klebanov-Strassler background these singularities cannot be cloaked by a horizon, which strongly suggests they are not physical. In this note we provide an analytic proof that the singularity of all codimension-three antibrane solutions (such as anti-D6 branes in massive type IIA supergravity or anti-D3 branes smeared on the T^3 of R^3xT^3 with fluxes) cannot be hidden behind a horizon, and that the charge of black branes with smooth event horizons must have the same sign as the charge of the flux background. Our result indicates that infinitesimally blackening the antibranes immediately triggers brane-flux annihilation, and strengthens the intuition that antibranes placed in flux with positive charge immediately annihilate against it.

Figures (1)

• Figure 1: The possible $\alpha$ profiles for solutions that have positive charge dissolved in fluxes at large radius (positive $\alpha$). Only when the derivative of $\alpha$ is positive at the origin a curve exists that vanishes at the origin (left plot). Curves with negative derivative at the origin necessarily must have some non-zero value for $\alpha$ at the origin (middle plot). If one insists on $\alpha$ having a negative derivative at zero, then it must have a turnaround point at some radius where $\alpha$ is negative, which is forbidden by Eq. (\ref{['topological']}), as shown in the right plot.