TY - JOUR AB - 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. AU - de,Rham C AU - Matas,A AU - Ondo,NA AU - Tolley,AJ DO - 17/175008 PY - 2015/// SN - 0264-9381 TI - Interactions of charged spin-2 fields T2 - Classical and Quantum Gravity UR - http://dx.doi.org/10.1088/0264-9381/32/17/175008 UR - http://hdl.handle.net/10044/1/51749 VL - 32 ER -