Another possibility is that we are “stuck” in a 3+1 dimensional (three spatial dimensions plus one time dimension) subspace of the full universe. Properly localized matter and Yang–Mills gauge fields will typically exist if the sub-spacetime is an exceptional set of the larger universe. These “exceptional sets” are ubiquitous in Calabi–Yau n-folds and may be described as subspaces without local deformations, akin to a crease in a sheet of paper or a crack in a crystal, the neighborhood of which is markedly different from the exceptional subspace itself. However, until the work of Randall and Sundrum, it was not known that gravity can be properly localized to a sub-spacetime. In addition, spacetime may be stratified, containing strata of various dimensions, allowing us to inhabit the 3+1-dimensional stratum—such geometries occur naturally in Calabi–Yau compactifications. Such sub-spacetimes are D-branes, hence such models are known as brane-world scenarios.