Brane polarization is no cure for tachyons

TL;DR

The paper shows that brane polarization cannot cure brane-brane-repelling tachyons in the studied setups. By deriving and analyzing the polarization potential for non-spherical D3-brane shells, the authors demonstrate a universal P-wave instability (the a^2 term is negative for all tachyon strengths) and a D-wave instability that arises when the tachyon mass exceeds a threshold $m > \frac{3}{2} C$. Consequently, anti-D3 branes polarized into NS5 branes at the bottom of the Klebanov-Strassler solution are unstable in the presence of such tachyons. These results suggest that metastable polarized vacua may be precluded in broad classes of tachyonic brane configurations and motivate a comprehensive analysis of all possible polarization channels and their stability.

Abstract

Anti-M2 and anti-D3 branes placed in regions with charges dissolved in fluxes have a tachyon in their near-horizon region, which causes these branes to repel each other. If the branes are on the Coulomb branch this tachyon gives rise to a runaway behavior, but when the branes are polarized into five-branes this tachyon only appears to lower the energy of the polarized branes, without affecting its stability. We analyze brane polarization in the presence of a brane-brane-repelling tachyon and show that when the branes are polarized along the direction of the tachyon the polarized shell is unstable. This implies that tachyons cannot be cured by brane polarization and indicates that, at least in a certain regime of parameters, anti-D3 branes polarized into NS5 branes at the bottom of the Klebanov-Strassler solution have an instability.

Figures (1)

• Figure 1: The graph shows the $a^2$ term of the polarization potential $v_2(\omega)$ (with $\omega \equiv m/C$), which is always negative.