# On two-vierbein gravity action from gauge theory of conformal group

## TL;DR

This paper explores a gravity theory derived from two gauge fields associated with the conformal group, analyzing their linearized equations around different backgrounds and identifying novel differences from Einstein and conformal gravity.

## Contribution

It introduces a two-vierbein gravity action from conformal gauge theory, analyzing its linearized equations and differences from established gravity theories.

## Key findings

- Linearized equations differ from Einstein and conformal gravity.
- Perturbations around Anti-de Sitter space reveal unique dynamics.
- Various configurations of gauge fields lead to distinct linearized behaviors.

## Abstract

We study the gravity action built from two gauge fields corresponding to the generators of the conformal group. Starting with the action from which one can obtain Einstein gravity and conformal gravity upon imposing suitable constraints, we keep two independent gauge fields and integrate out the field corresponding to the generator of Lorentz transformations. We identify the two gauge fields with two vierbeins and perturb them around an Anti--de Sitter space. This gives the linearized equations that differ from both, Einstein gravity and conformal gravity linearized equations. We also study the linearized equations for one gauge field perturbed around the flat space and one around zero, and the case when the gauge fields are proportional to each other.