Deconstructing Dimensions and Massive Gravity

TL;DR

This paper demonstrates that ghost-free massive gravity models can be derived from higher-dimensional General Relativity through a discrete extra dimension, linking Dimensional Deconstruction with Kaluza-Klein truncation and analyzing their physical implications.

Contribution

It establishes a connection between ghost-free massive gravity and higher-dimensional GR via Dimensional Deconstruction, clarifying the role of Kaluza-Klein truncation and IR physics.

Findings

Dimensional Deconstruction is equivalent to nonlinear Kaluza-Klein truncation.

A low strong coupling scale depends on IR physics and affects the Vainshtein mechanism.

Continuous extra dimensions do not recover higher-dimensional gravity due to strong coupling issues.

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.