Interactions of charged spin-2 fields

Claudia De Rham, Andrew Matas, Nicholas A. Ondo, Andrew J. Tolley

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9 Scopus citations


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 languageEnglish (US)
Article number175008
JournalClassical and Quantum Gravity
Issue number17
StatePublished - Sep 10 2015

Bibliographical note

Publisher Copyright:
© 2015 IOP Publishing Ltd.


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


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