Higher dimensional gravity invariant under the AdS group

TL;DR

This paper constructs a higher-dimensional gravity action invariant under both local Lorentz and AdS boost symmetries, applicable in odd and even dimensions, matching coefficients from previous work.

Contribution

It introduces a new class of gravity actions invariant under extended symmetries in higher dimensions, aligning with prior results by Troncoso and Zanelli.

Findings

Invariant gravity actions exist in all dimensions

Actions match coefficients from Troncoso and Zanelli

Construction applies to both odd and even dimensions

Abstract

A higher dimensional gravity invariant both under local Lorentz rotations and under local Anti de Sitter boosts is constructed. It is shown that such a construction is possible both when odd dimensions and when even dimensions are considered. It is also proved that such actions have the same coefficients as those obtained by Troncoso and Zanelli.