Interacting Lagrangian for massive spin-two field

As is well known, Kaluza-Klein compactification of five-dimensional gravity gives a four-dimensional theory of a tower of massive spin-2 fields interacting with background gravitational, electromagnetic, and scalar fields. Working to lowest order in the massive fields, one can obtain a Lagrangian for a single massive spin-2 field interacting with gravitational and other background fields which is consistent up to terms of higher order in the massive spin-2 field. This consistency depends on massive spin-2 gauge invariances which are valid up to terms of higher order in the massive field. We explicitly exhibit the four-dimensional Lagrangian and its gauge transformations. This analysis parallels a similar analysis in string theory carried out elsewhere