Deconstructing dimensions and massive gravity

We show that the ghost-free models of massive gravity and their multi-graviton extensions follow from considering higher dimensional General Relativity in Einstein-Cartan form on a discrete extra dimension, according to the dimensional deconstruction paradigm. We show that dimensional deconstruction is equivalent to a truncation of the Kaluza-Klein tower at the nonlinear level. Higher dimensional gravity is not recovered from a lower dimensional multi-graviton theory in the limit of a continuous extra dimension (infinite Kaluza-Klein tower) due to the appearance of a low strong coupling scale that depends on IR physics. This strong coupling scale, which is associated with the mass of the lowest Kaluza-Klein mode, controls the onset of the Vainshtein mechanism and is crucial to the theoretical and observational viability of the truncated theory.