Tachyonic Anti-M2 Branes

TL;DR

This work analyzes fully back-reacted anti-M2 branes in the CGLP/Stenzel background, showing that the energy-density singularity of the four-form flux persists beyond perturbation theory. It examines resolution via M5 polarization, finding no transverse minimum for smeared anti-M2s, and extends to localized branes to compute the Klebanov-Pufu channel potential, revealing a tachyonic r^2 term that induces repulsion between anti-M2 stacks. The results imply a tachyonic instability of anti-M2 branes in flux backgrounds with opposite-charge sources, suggesting fragmentation or rapid brane-flux annihilation as end-points, and cast doubt on the robustness of metastable anti-brane constructions in these settings. The findings have broad implications for holographic SUSY-breaking scenarios and the stability of warped throat constructions in string theory, and motivate further analyses of backreacted anti-brane systems across backgrounds.

Abstract

We study the dynamics of anti-M2 branes in a warped Stenzel solution with M2 charges dissolved in fluxes by taking into account their full backreaction on the geometry. The resulting supergravity solution has a singular magnetic four-form flux in the near-brane region. We examine the possible resolution of this singularity via the polarization of anti-M2 branes into M5 branes, and compute the corresponding polarization potential for branes smeared on the finite-size four-sphere at the tip of the Stenzel space. We find that the potential has no minimum. We then use the potential for smeared branes to compute the one corresponding to a stack of localized anti-M2 branes, and use this potential to compute the force between two anti-M2 branes at tip of the Stenzel space. We find that this force, which is zero in the probe approximation, is in fact repulsive. This surprising result points to a tachyonic instability of anti-M2 branes in backgrounds with M2 brane charge dissolved in flux.

Figures (4)

• Figure 1: Anti-M2 branes smeared over (left) and localized at a point (right) on the 4-sphere at the apex of the 8-dimensional Stenzel space.
• Figure 2: In the interval $\rho_1 < \rho < \rho_2$ (marked in light grey) the energy of the SD flux is small compared to that of the electric flux of the anti-M2 branes and therefore can be treated perturbatively. The (UV) scale where this anti-M2 region is "glued" to the (self-dual) CGLP solution is $\rho_2$, and the (IR) scale where the backreaction of the SD flux becomes important is $\rho_1$. When the $\overline{\rm M2}$ sources are localized these slicings will be deformed and will have a non-trivial angular dependence.
• Figure 3: For anti-M2 branes localized on the 4-sphere the gluing between the brane-dominated and the asymptotically-CGLP regions will not be at constant $\rho_2$. However, we can always push this hypersurface away from the tip (arrows pointing right) by increasing $N_{\overline{\textrm{M2}}}$, and push it towards the tip (arrows pointing left) by increasing $M$. If the size of the tip is much smaller than $\rho_2$, then localizing the branes will not affect this surface.
• Figure 4: The naive polarization potential one derives ignoring the anti-M2 backreaction Klebanov:2010qs (first graph), the potential one obtains by (incorrectly) assuming that backreaction will give rise to an attractive force between the anti-branes (second graph) and the two possible corrected potentials obtained by including the anti-M2 tachyon. If $\theta_\star$ is larger than $\theta_\textrm{curv}$, than the tachyonic $-\theta^2$ mode can wipe out the local minimum (third graph). We can reduce $\theta_\star$ by considering polarization into multiple M5 branes, guaranteeing this way a metastable minimum at the $\theta=\theta_\star$ scale (fourth graph). As we explain in the text, the tachyonic mode can greatly change the physics of this metastable vacuum, by opening up new instability directions.