Interacting Spin-2 Fields
Kurt Hinterbichler, Rachel A. Rosen
TL;DR
The paper tackles the Boulware-Deser ghost problem in interacting spin-2 theories and demonstrates that a vielbein formulation yields an extra primary constraint that removes the ghost to all orders in $D$-dimensional spacetime, including beyond any decoupling limit.It introduces a general multi-metric framework with ${ m cal N}$ spin-2 fields and a wedge-product ghost-free potential $U$, which, together with a Hamiltonian analysis in the upper-triangular vielbein gauge, yields the necessary constraints for ghost-freedom on arbitrary interaction graphs.For ${ m cal N}=2$, the vielbein formulation is shown to be dynamically equivalent to the standard metric theories of ghost-free bi-gravity and dRGT massive gravity, while for more fields it provides a straightforward path to ghost-free multi-metric interactions through symmetric-polynomial structures and theory-graph representations.The work broadens the parameter space of consistent spin-2 theories, offering a conceptually clear and technically robust framework that could address issues such as superluminality and EFT cutoffs, and motivates further study of multi-metric couplings and matter interactions in the vielbein language.
Abstract
We construct consistent theories of multiple interacting spin-2 fields in arbitrary spacetime dimensions using a vielbein formulation. We show that these theories have the additional primary constraints needed to eliminate potential ghosts, to all orders in the fields, and to all orders beyond any decoupling limit. We postulate that the number of spin-2 fields interacting at a single vertex is limited by the number of spacetime dimensions. We then show that, for the case of two spin-2 fields, the vielbein theory is equivalent to the recently proposed theories of ghost-free massive gravity and bi-metric gravity. The vielbein formulation greatly simplifies the proof that these theories have an extra primary constraint which eliminates the Boulware-Deser ghost.