A new type of gauge invariance for a collection of massless spin-2 fields. I. Existence and uniqueness

It has been shown that the most general type of gauge invariance for a single massless spin-2 field is either 'normal' spin-2 gauge invariance or general covariance. The authors extend that analysis to the case of a collection of spin-2 fields. They obtain the general solution of the integrability condition which determines whether a given candidate infinitesimal symmetry arises from an exact symmetry. This general solution is a new type of gauge invariance involving associative commutative algebras in a manner analogous to the way gauge symmetries of collections of spin-1 fields are based on Lie algebras.