## Abstract

In light of recent progress in ghost-free theories of massive gravity and multi-gravity, we reconsider the problem of constructing a ghost-free theory of an interacting spin-2 field charged under a U(1) gauge symmetry. Our starting point is the theory originally proposed by Federbush, which is essentially Fierz-Pauli generalized to include a minimal coupling to a U(1) gauge field. We show the Federbush theory with a dynamical U(1) field is in fact ghost-free and can be treated as a healthy effective field theory to describe a massive charged spin-2 particle. It can even potentially have healthy dynamics above its strong-coupling scale. We then construct candidate gravitational extensions to the Federbush theory both by using dimensional deconstruction, and by constructing a general nonlinear completion. However, we find that the U(1) symmetry forces us to modify the form of the Einstein-Hilbert kinetic term. By performing a constraint analysis directly in the first-order form, we show that these modified kinetic terms inevitably reintroduce the Boulware-Deser ghost. As a by-product of our analysis, we present a new proof for ghost-freedom of bi-gravity in 2+1 dimensions (also known as Zwei-Dreibein gravity). We also give a complementary algebraic argument that the Einstein-Hilbert kinetic term is incompatible with a U(1) symmetry, for a finite number of gravitons.

Original language | English (US) |
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Article number | 175008 |

Journal | Classical and Quantum Gravity |

Volume | 32 |

Issue number | 17 |

DOIs | |

State | Published - Sep 10 2015 |

### Bibliographical note

Publisher Copyright:© 2015 IOP Publishing Ltd.

## Keywords

- charged spin-2 fields
- deconstruction
- multi-gravity