Membranes with topological charge and AdS4/CFT3 correspondence

If the second Betti number b2 of a Sasaki-Einstein manifold Y7 does not vanish, then M-theory on AdS4×Y7 possesses "topological" U(1)b2 gauge symmetry. The corresponding Abelian gauge fields come from three-form fluctuations with one index in AdS4 and the other two in Y7. We find black membrane solutions carrying one of these U(1) charges. In the zero-temperature limit, our solutions interpolate between AdS4×Y7 in the UV and AdS2×R2×squashedY7 in the IR. In fact, the AdS2×R2× squashedY7 background is by itself a solution of the supergravity equations of motion. These solutions do not appear to preserve any supersymmetry. We search for their possible instabilities and do not find any. We also discuss the meaning of our charged membrane backgrounds in a dual quiver Chern-Simons gauge theory with a global U(1) charge density. Finally, we present a simple analytic solution which has the same IR but different UV behavior. We reduce this solution to type IIA string theory, and perform T-duality to type IIB. The type IIB metric turns out to be a product of the squashed Y7 and the extremal Bañados-Teitelboim-Zanelli black hole. We discuss an interpretation of this type IIB background in terms of the (1+1)-dimensional conformal field theory on D3-branes partially wrapped over the squashed Y7.