  Einstein-Gauss-Bonnet gravity in five-dimensional spacetime provides an
excellent example of a theory that, while including higher-order curvature
corrections to General Relativity, still shares many of its features, such as
second-order field equations for the metric. We focus on the largely unexplored
case where the coupling constants of the theory are such that no
constant-curvature solution is allowed, leaving open the question of what the
vacuum state should then be. We find that even a slight deviation from the
anti-de Sitter Chern-Simons theory, where the vacuum state is five-dimensional
AdS spacetime, leads to a complete symmetry breakdown, with the fifth dimension
either being compactified into a small circle or shrinking away exponentially
with time. A complete family of solutions, including duality relations among
them, is uncovered and shown to be unique within a certain class. This
dynamical dimensional reduction scenario seems particularly attractive as a
means for higher-dimensional theories to make contact with our four-dimensional
world.
