Interactions of charged spin-2 fields. (10th August 2015)

• Record Type: Journal Article
• Authors: Rham, Claudia de; Matas, Andrew; Ondo, Nicholas A; Tolley, Andrew J
• Is Part Of: Classical and quantum gravity. Volume 32:Number 17(2015:Sep.)
• Publication Date: 2015-08-10
• Subjects: multi-gravity -- deconstruction -- charged spin-2 fields; Quantum gravity -- Periodicals; Gravitation -- Periodicals; Relativity (Physics) -- Periodicals; Space and time -- Periodicals; Periodicals; 521.1
• DOI: 10.1088/0264-9381/32/17/175008
• Languages: English
• ISSNs: 0264-9381

Abstract

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.