Parity violating spin-two gauge theories

TL;DR

This paper explores nonlinear, parity-violating deformations of free spin-two gauge theories in higher dimensions, revealing novel algebra-valued theories in 3 and 5 dimensions with implications for energy positivity and dimensional reduction.

Contribution

It identifies and explicitly constructs all second-order quasilinear parity-violating deformations of spin-two gauge theories in dimensions greater than two, especially detailing the n=5 case.

Findings

New algebra-valued spin-two gauge theories in 3 and 5 dimensions.

Complete all-order deformation in 5 dimensions.

Kaluza-Klein reduction yields coupled spin-two, spin-one, and spin-zero fields.

Abstract

Nonlinear covariant parity-violating deformations of free spin-two gauge theory are studied in n>2 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 and n=5 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 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 5-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 dimensions is derived, giving a parity-violating nonlinear gauge theory of a coupled set of spin-two, spin-one, and spin-zero massless fields.