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

TL;DR

This paper derives the superpotential for a supersymmetric M-theory solution with a Stenzel space and analyzes the backreaction of anti-M2 branes, revealing potential singularities that challenge the existence of metastable vacua in such setups.

Contribution

It provides the first detailed supergravity analysis of anti-M2 brane backreaction in a warped Stenzel space, including solving coupled equations and examining singularities.

Findings

Backreacted solutions exhibit infrared singularities.

Singularities cast doubt on the metastability of anti-brane configurations.

Results support similar issues found in anti-D3 branes in warped throats.

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.