Multigravity from a discrete extra dimension

TL;DR

This paper develops a multigravity model from discretizing a five-dimensional gravitational theory, maintaining key symmetries, and demonstrates the absence of ghosts and massive modes through symmetry analysis.

Contribution

It introduces a discretization approach that preserves four-dimensional diffeomorphism invariance and relates Goldstone bosons to shift fields, ensuring ghost-free scalar excitations.

Findings

No ghosts or massive modes in the discretized theory

Maintains four-dimensional diffeomorphism invariance on each site

Establishes a connection between Goldstone bosons and shift fields

Abstract

Multigravity theories are constructed from the discretization of the extra dimension of five dimensional gravity. Using an ADM decomposition, the discretization is performed while maintaining the four dimensional diffeomorphism invariance on each site. We relate the Goldstone bosons used to realize nonlinearly general covariance in discretized gravity to the shift fields of the higher dimensional metric. We investigate the scalar excitations of the resulting theory and show the absence of ghosts and massive modes; this is due to a local symmetry inherited from the reparametrization invariance along the fifth dimension.