Chiral description of ghost-free massive gravity

We propose and study a new first order version of the ghost-free massive gravity. Instead of metrics or tetrads, it uses a connection together with Plebanski's chiral 2-forms as fundamental variables, rendering the phase space structure similar to that of SU(2) gauge theories. The chiral description simplifies computations of the constraint algebra, and allows us to perform the complete canonical analysis of the system. In particular, we explicitly compute the secondary constraint and carry out the stabilization procedure, thus proving that in general the theory propagates 7 degrees of freedom, consistently with previous claims. Finally, we point out that the description in terms of 2-forms opens the door to an infinite class of ghost-free massive bi-gravity actions. Our results apply directly to Euclidean signature. The reality conditions to be imposed in the Lorentzian signature appear to be more complicated than in the usual gravity case and are left as an open issue.

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