Abstract
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 $$ \overline N $$ backreacting anti-M2 branes by fixing all the 12 integration constants in terms of $$ \overline N $$ . 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.
Highlights
Given the difficulties in proving this, we will assume that the singularity is harmless and we will try to see if the anti-M2 solution develops problems in the UV; if this is not the case, the solution we find describes the holographic dual of the conjectured metastable state in the field theory, but clearly a more detailed study of the IR singularity is required to decide whether this supergravity solution can be trusted or not
In this paper we constructed the analytic solution for the twelve-dimensional space of linearized non-supersymmetric deformations of the warped Stenzel space, consistent with the SO(5) symmetries of the supersymmetric background
We were interested in finding the supergravity solution dual to metastable states, which were conjectured in [10] to be described by a stack of anti-M2 branes placed at the tip of the transverse geometry
Summary
The linearized equations governing the deformations around the warped Stenzel space have been derived in [13] by using the Borokhov-Gubser [14] first-order formalism. Where X represents the set of perturbation parameters, φa is linear in them, and φa0 are the functions in the CGLP solution, written explicitly in (2.15). The first order formalism gives a set of 2n linear first-order differential equations for the perturbations φa and their conjugates ξa: dξa dτ ξb. As shown in [13], it is useful to solve for the following linear combinations of the fields ξa and φa ξa = (ξ1 + ξ2 + ξ3, ξ1 − ξ2 + 3 ξ3, ξ1 + ξ2 − 3ξ3, ξ4, ξ5, ξ6) , φa = (φ1 − φ2, φ1 + φ2 − 2 φ3, φ3, φ4, φ5, φ6). The first-order systems of coupled differential equations for the fields ξa and φa are: ξ4. + 18(h0(−3(f0 − 2h0)(2φ3 + φ4) + φ5) + (f0 − 4h0)φ6))
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