The Backreaction of Anti-M2 Branes on a Warped Stenzel Space

TL;DR

This work analyzes the backreaction of smeared anti-M2 branes at the bottom of the warped Stenzel-CGLP background in M-theory. By deriving a superpotential for the SUSY background and applying the Borokhov–Gubser first-order formalism, the authors reduce the perturbation problem to linear first-order equations for conjugate momenta $\xi_a$ and perturbations $\phi^a$, and obtain analytic and asymptotic solutions for the perturbations. They compute the force on a probe M2 brane, showing it depends only on the $\tilde{\xi}_4$ mode, and analyze the full IR/UV structure, including normalizable vs non-normalizable modes with operator dimensions $\Delta = 3,4,5,6,7/3$ in the dual theory. Crucially, the anti-M2 backreaction that yields a nonzero force requires an infrared singularity in the warp factor and $G_4$ energy density, mirroring the anti-D3/KS situation, which argues against metastable vacua in this setup unless the singularity is deemed physical.

Abstract

We find the superpotential governing the supersymmetric warped M-theory solution with a transverse Stenzel space found by Cvetic, Gibbons, Lu and Pope in hep-th/0012011, and use this superpotential to extract and solve the twelve coupled equations underlying the first-order backreacted solution of a stack of anti-M2 branes in this space. These anti-M2 branes were analyzed recently in a probe approximation by Klebanov and Pufu, who conjectured that they should be dual to a metastable vacuum of a supersymmetric 2+1 dimensional theory. We find that the would-be supergravity dual to such a metastable vacuum must have an infrared singularity and discuss whether this singularity is acceptable or not. Given that a similar singularity appears when placing anti-D3 branes in the Klebanov-Strassler solution, our work strengthens the possibility that anti-branes in warped throats do not give rise to metastable vacua.