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 $S^{d-3}\times R$ or $H^{d-3}\times R$. The configurations with an event horizon topology $S^{d-2}\times S^1$ 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.