Density functional for hard hyperspheres from a tensorial-diagrammatic series

We represent the free energy functional by a diagrammatic series with tensorial coefficients indexed by powers of the length scale. For hard cores, we obtain Percus's exact functional in one dimension and the Kierlik-Rosinberg form of fundamental measures theory in three dimensions. In five dimensions, the functional describes bulk fluids better than does the Percus-Yevick theory. At planar walls, density profiles oscillate with smaller periods than in lower dimensions. Our findings open up avenues for treating both more general high-dimensional systems and three-dimensional mixtures via dimensional reduction.