Metric Formulation of Ghost-Free Multivielbein Theory

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.