Abstract
We obtain finite-temperature M2 black branes in 11-dimensional supergravity, in a G4-flux background whose self-dual part approaches a solution of Cvetič, Gibbons, Lü, and Pope, based upon Stenzel’s family of Ricci-flat Kähler deformed cones. Our solutions are asymptotically AdS4 times a 7-dimensional Stiefel manifold V5,2, and the branes are "smeared" to retain SO(5) symmetry in the internal space. The solutions represent a mass deformation of the corresponding dual CFT3, whose full description is at this time only partially-understood. We investigate the possibility of a confinement/de-confinement phase transition analogous to the AdS5 × S5 case, and a possible Gregory-Laflamme type instability which could lead to polarised brane solutions which break SO(5). We discuss possible consequences for AdS/CFT and the KKLT cosmological uplift mechanism.
Highlights
If the charge at the horizon is the same sign as at infinity for all solutions, it means that the singularities of smeared anti-branes added to the CGLP solution cannot be cloaked with a finite-temperature horizon
AdS4 × V5,2 black branes in 11-dimensional supergravity provide a fertile ground for theoretical study, encompassing such diverse topics as novel black brane solutions in higher dimensions, thermodynamics of 2+1 dimensional CFTs, and the KKLT proposal for building de Sitter solutions in string theory
In this work we have tried to emphasise the connections between these different perspectives in the context of black brane solutions in the CGLP flux background
Summary
Throughout this paper we will work in 11 dimensional supergravity, whose action is. where G(4) = dA(3) and R is the Ricci scalar (and 1 = vol is the volume form). Where ds is an 8-dimensional manifold that is topologically a Stenzel space (i.e. a deformed cone over the Stiefel manifold V5,2 as in the CGLP solution [9]), but on which certain squashing modes of the V5,2 have been turned on. There is a conical singularity at r = 0, which can be smoothed out by blowing it up into a sphere (in our case an S4), yielding the n = 3 Stenzel space This is called “deformation of the cone”, and lower-dimensional analogues include the deformed conifold (n = 2), and the Eguchi-Hanson instanton (n = 1). We will be interested in brane-flux solutions where the 8-dimensional metric ds in (2.5) takes the form of the Stenzel ansatz (2.12); the squashing functions a, b, c will change in order to accommodate a black-hole horizon at some value of τ.
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