Metric Formulation of Ghost-Free Multivielbein Theory

TL;DR

This paper reformulates ghost-free multivielbein theory using metrics, preserving ghost-free properties and demonstrating equivalence between metric and vielbein descriptions through explicit gauge fixing.

Contribution

It introduces a metric formulation of ghost-free multivielbein theory by restoring local Lorentz invariance, ensuring the theory remains ghost-free and establishing equivalence with the vielbein approach.

Findings

The metric formulation maintains ghost-free properties.

Explicit gauge fixing separates gauge degrees of freedom.

On-shell equivalence between metric and vielbein descriptions.

Abstract

We formulate the recently proposed ghost-free theory of multiple interacting vielbeins in terms of their corresponding metrics. This is achieved by reintroducing all local Lorentz invariances broken by the multivielbein interaction potential which, in turn, allows us to explicitly separate the gauge degrees of freedom in the vielbeins from the components of the metrics by an appropriate gauge choice. We argue that the gauge choice does not spoil the no-ghost proof of the multivielbein theory, hence the multimetric theory is ghost-free. We further show the on-shell equivalence of the metric and vielbein descriptions, first in general and thereafter in two illustrative examples.