Parity violating spin-two gauge theories

Nonlinear covariant parity-violating deformations of free spin-two gauge theory are studied in $n>~3$ spacetime dimensions, using a linearized frame and spin-connection formalism, for a set of massless spin-two fields. It is shown that the only such deformations yielding field equations with a second order quasilinear form are the novel algebra-valued types in $n=3\mathrm{}$ and $n=5\mathrm{}$ dimensions already found in some recent related work concentrating on lowest order deformations. The complete form of the deformation to all orders in $n=5\mathrm{}$ dimensions is worked out here and some features of the resulting new algebra-valued spin-two gauge theory are discussed. In particular, the internal algebra underlying this theory on five-dimensional Minkowski space is shown to cause the energy for the spin-two fields to be of indefinite sign. Finally, a Kaluza-Klein reduction to $n=4\mathrm{}$ dimensions is derived, giving a parity-violating nonlinear gauge theory of a coupled set of spin-two, spin-one, and spin-zero massless fields.