Effectively four-dimensional spacetimes emerging from d = 5 Einstein–Gauss–Bonnet gravity

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.