Deconstructing Dimensions and Massive Gravity

TL;DR

This work shows that ghost-free massive gravity, its bigravity, and multi-gravity extensions can be derived from five-dimensional General Relativity in Einstein-Cartan form on a discrete extra dimension via Dimensional Deconstruction. The authors demonstrate a nonlinear equivalence between Dimensional Deconstruction and a truncated Kaluza-Klein tower, yielding ghost-free mass terms through a vielbein discretization that produces the square-root structure characteristic of dRGT theories. A central result is the identification of a low strong-coupling scale set by IR physics (the size of the extra dimension), which governs the onset of the Vainshtein mechanism and obstructs a smooth continuum limit to 5D GR when the lapse is fixed; keeping the lapse dynamical could, in principle, allow a continuum limit but introduces new degrees of freedom and challenges ghost-freedom. These findings illuminate the tension between achieving ghost-free four-dimensional multi-gravity descriptions and recovering genuine five-dimensional General Relativity, with implications for how matter might couple to multiple metrics and for potential extensions to more elaborate extra-dimensional setups.

Abstract

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.