Gravity with antisymmetric components

Abstract

This work proposes a new gravitational theory formulated in terms of the vierbein field. The vierbein contains components which can be shifted by local Lorentz transformations and therefore do not show up in the spacetime metric. These components are given dynamics and become physical in our setup. They enter the massless theory in the form of an antisymmetric tensor field which makes the action reminiscent of the bosonic sector of supergravity. We then demonstrate that both the metric and the antisymmetric tensor can be made massive by adding a potential term for the vierbein. The form of this mass potential is inspired by ghost-free massive gravity. We confirm the absence of additional and potentially pathological degrees of freedom in an ADM analysis. However, at the linearized level around maximally symmetric solutions, the fluctuation of the antisymmetric tensor has a tachyonic mass pole.

Vierbein interactions with antisymmetric components

“…We demonstrate that the action proposed in [28] can be generalized to a fully dynamical theory for two interacting vierbein fields e a m and e a m . The result is a ghost-free bimetric action in vierbein formulation with dynamical Lorentz components which we parameterize in terms of the antisymmetric components The action is manifestly invariant under local Lorentz transformations and diffeomorphisms.…”

“…Interestingly, the consistency problem of non-vanishing Lorentz components can be overcome by giving them a kinetic term 2 . This was demonstrated explicitly in [28] for the case of a fixed reference frame field e a m (i.e. for the massive gravity case).…”

“…We have generalized the massive gravity theory with dynamical antisymmetric components proposed in [28] to the case with a dynamical reference frame e a m . The difference of the model with fixed reference frame and the fully dynamical setup is similar to the difference of massive gravity with a fixed fiducial metric and bimetric theory with two dynamical tensor fields.…”

“…In [28], we repackaged the 10+6 components contained in the tensor fields into the vierbein e a m . This was achieved by making the following identifications,…”

“…In this work we will build on the results of [28] and extend the setup by giving dynamics to the frame field e a m .…”