Metastable Vacua and the Backreacted Stenzel Geometry

Abstract

We construct an M-theory background dual to the metastable state recently discussed by Klebanov and Pufu, which corresponds to placing a stack of anti-M2 branes at the tip of a warped Stenzel space. With this purpose we analytically solve for the linearized non-supersymmetric deformations around the warped Stenzel space, preserving the SO(5) symmetries of the supersymmetric background, and which interpolate between the IR and UV region. We identify the supergravity solution which corresponds to a stack of $\bar{N}$ backreacting anti-M2 branes by fixing all the 12 integration constants in terms of $\bar{N}$. While in the UV this solution has the desired features to describe the conjectured metastable state of the dual (2+1)-dimensional theory, in the IR it suffers from a singularity in the four-form flux, which we describe in some details.

Figures (3)

• Figure 1: The solution for the mode $\tilde{\phi}_6$, for $X_2=0$, $X_1=X_3=X_5=X_6=1$, $X_4=10$, $Y_a=1$, $m=1$ (underlying blue solid line). The red and orange dashed curves correspond to the IR and UV expansions (respectively up to 20 and 15 terms).
• Figure 2: The profile of the M2 charge $Q_{M2}$ for the BPS perturbation, for different values of the parameter $Y_6$. The black dashed line is the zeroth--order solution ($Y_6=0$). Note that at the linearized level the perturbations vanish in the UV.
• Figure 3: The profile of the first--order M2 charge $Q_{M2}^{(1)}$ for the anti--M2 solution, setting $\bar{N} =1$.