Membranes with Topological Charge and AdS4/CFT3 Correspondence

TL;DR

This paper constructs black membrane solutions in M-theory on AdS_4 x Y^7 with topological U(1) charges, explores their IR and UV limits, and discusses their dual CFT interpretations, including a type IIB background related to wrapped D3-branes.

Contribution

It introduces new charged membrane solutions in M-theory with topological charges and analyzes their IR and UV behaviors, connecting supergravity solutions to dual CFTs and string theory backgrounds.

Findings

Existence of black membrane solutions with topological U(1) charges.

Solutions interpolate between AdS_4 and AdS_2 x R^2 x squashed Y^7.

Type IIB background related to wrapped D3-branes and BTZ black hole.

Abstract

If the second Betti number b_2 of a Sasaki-Einstein manifold Y^7 does not vanish, then M-theory on AdS_4 x Y^7 possesses "topological" U(1)^{b_2} gauge symmetry. The corresponding Abelian gauge fields come from three-form fluctuations with one index in AdS_4 and the other two in Y^7. We find black membrane solutions carrying one of these U(1) charges. In the zero temperature limit, our solutions interpolate between AdS_4 x Y^7 in the UV and AdS_2 x R^2 x squashed Y^7 in the IR. In fact, the AdS_2 x R^2 x squashed Y^7 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 Y^7 and the extremal BTZ black hole. We discuss an interpretation of this type IIB background in terms of the (1+1)-dimensional CFT on D3-branes partially wrapped over the squashed Y^7.