Membranes with topological charge and AdS(4)/CFT3 correspondence

作者：Klebanov Igor R^*; Pufu Silviu S; Tesileanu Tiberiu

来源：Physical Review D - Particles, Fields, Gravitation and Cosmology, 2010, 81(12): 125011.

DOI：10.1103/PhysRevD.81.125011

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)(b2) 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 Banados-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 Y-7.

• 出版日期2010-6-14