Kaluza-Klein towers on general manifolds

A higher dimensional universe with compactified extra dimensions admits a four-dimensional description consisting of an infinite Kaluza-Klein tower of fields. We revisit the problem of describing the free part of the complete Kaluza-Klein tower of gauge fields, $p$ forms, gravity, and flux compactifications. In contrast to previous studies, we work with a generic internal manifold of any dimension, completely at the level of the action, in a gauge-invariant formulation and without resorting to the equations of motion or analysis of propagators. We demonstrate that the physical fields and St\"uckelberg fields are naturally described by ingredients of the Hodge decomposition and its analog for symmetric tensors. The spectrum of states and stability conditions, in terms of the eigenvalues of various Laplacians on the internal manifold, is easily read from the action.