Consistent interacting massive spin-2 requires an infinity of states

Abstract

Although Kaluza-Klein compactification provides a way of consistently coupling massive spin-2 fields to gravity, it does so by having infinite towers of massive states. Consistency is achieved by virtue of a corresponding infinite number of four-dimensional gauge invariances. We explicitly demonstrate that any attempt to truncate to a finite number of massive spin-2 fields leads to an explicit breaking of all the massive gauge invariances, including those for the massive fields that are retained. Therefore attempts to use the truncation of a Kaluza-Klein theory as a way to obtain a lagrangian with a finite number of massive spin-2 fields interacting consistently with gravity will inevitably fail.