We construct a general class of exact regular black hole solutions with toroidal horizon topology in five-dimensional anti–de Sitter gravity with a self-interacting scalar field. With these boundary conditions and due to the nontrivial backreaction of the scalar field, the no-hair theorems can be evaded so that an event horizon can be formed. The scalar field is regular everywhere outside the curvature singularity and it vanishes at the boundary where the potential is finite. We study the properties of these black holes in the context of AdS/CFT duality and comment on the dual operators, which saturate the unitarity bound. We present exact expressions for the beta function and construct a $c$-function that characterizes the renormalization-group flow.

• Received 17 December 2012

DOI:https://doi.org/10.1103/PhysRevD.87.124033