An exotic theory of massless spin–two fields in three dimensions†

It is a general belief that the only possible way to consistently deform the Pauli– Fierz action, changing also the gauge algebra, is general relativity. Here we show that a different type of deformation exists in three dimensions if one allows for PT non–invariant terms. The new gauge algebra is different from that of diffeomorphisms. Furthermore, this deformation can be generalized to the case of a collection of massless spin–two fields. In this case it describes a consistent interaction among them. 1 ”Chercheur F.R.I.A.”, Belgium.