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.
Highlights
Anti-branes in warped throat geometries are an important ingredient in many models of supersymmetry breaking in string theory
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
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
Summary
Anti-branes in warped throat geometries are an important ingredient in many models of supersymmetry breaking in string theory. The supergravity solution corresponding to the anti-M2 branes (smeared over the four sphere at the tip of the cone) has been constructed later in [11, 12], by treating the anti-M2 perturbation as a small, first-order deformation of the supersymmetric CGLP background While this solution has the expected UV properties to correspond to a metastable state, the energy density of the four-form flux diverges in the infrared, near-brane region. For M2 branes localized on the CGLP infrared S4, these channels correspond to the Klebanov-Pufu M5 brane and to a transverse M5 brane that wraps the contractible S3 of the CGLP solution at a finite distance away from the tip Since this polarization channel is not wiped out by smearing the anti-M2 branes on the S4, we can use our fully-back-reacted solution to calculate its polarization potential. Further technical details and discussions are left to the appendices
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