Black string solutions with negative cosmological constant

We present arguments for the existence of new black string solutions with negative cosmological constant. These higher-dimensional configurations have no dependence on the 'compact' extra dimension, and their conformal infinity is the product of time and Sd-3 x R or Hd-3 x R. The configurations with an event horizon topology Sd-2 x S1 have a nontrivial, globally regular limit with zero event horizon radius. We discuss the general properties of such solutions and, using a counterterm prescription, we compute their conserved charges and discuss their thermodynamics. Upon performing a dimensional reduction we prove that the reduced action has an effective SL(2,R) symmetry. This symmetry is used to construct non-trivial solutions of the Einstein-Maxwell-Dilaton system with a Liouville-type potential for the dilaton in (d-1)-dimensions