A new spin-2 self-dual model in D=2+1
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There are three self-dual models of massive particles of helicity + 2 (or -2) in D = 2 + 1. Each model is of first, second, and third-order in derivatives. Here we derive a new self-dual model of fourth-order, L(SD)((4)), which follows from the third-order model (linearized topologically massive gravity) via Noether embedment of the linearized Weyl symmetry. In fact, each self-dual model can be obtained from the previous one L(SD)((i)) -> L(SD)((i+1)), i = 1, 2, 3 by the Noether embedment of an appropriate gauge symmetry, culminating in L(SD)((4)). The new model may be identified with the linearized version of L(HDTMG) = epsilon(mu nu rho)Gamma(epsilon)(mu gamma) [partial derivative(nu)Gamma(gamma)(epsilon rho) + (2/3)Gamma(gamma)(nu delta)Gamma(delta)(rho epsilon)]/8m + root-g[R(mu nu)R(nu mu) - 3R(2)/8]/2m(2). We also construct a master action relating the third-order self-dual model to L(SD)((4)) by means of a mixing term with no particle content which assures spectrum equivalence of L(SD)((4)) to other lower-order self-dual models despite its pure higher derivative nature and the absence of the Einstein-Hilbert action. The relevant degrees of freedom of L(SD)((4)) are encoded in a rank-two tensor which is symmetric, traceless and transverse due to trivial (non-dynamic) identities, contrary to other spin-2 self-dual models. We also show that the Noether embedment of the Fierz-Pauli theory leads to the new massive gravity of Bergshoeff, Hohm and Townsend.