Chiral description of ghost-free massive gravity

TL;DR

This paper introduces a new first order chiral formulation of ghost-free massive gravity using Plebanski's 2-forms and connections, simplifying the canonical analysis and confirming the theory propagates seven degrees of freedom.

Contribution

It presents a novel chiral first order framework for ghost-free massive gravity, enabling explicit constraint analysis and revealing potential for new ghost-free bi-gravity models.

Findings

Complete canonical analysis confirming 7 degrees of freedom

Explicit computation of secondary constraints

Identification of a new class of ghost-free bi-gravity actions

Abstract

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.