A new spin-2 self-dual model inD= 2+1

Abstract

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 (4) SD are encoded in a ranktwo 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.

Weyl and transverse diffeomorphism invariant spin-2 models in $$D=2+1$$ D = 2 + 1

“…Although LNMG can be obtained from the usual massive FP model via master action, see for instance [19], we have not been able to derive the WLNMG model from any secondorder theory. The WLNMG model contains both helicities +2 and −2, in the next subsection we look at parity singlets of helicity +2 or −2 described in terms of a symmetric traceless tensor.…”

“…The SDn model can be obtained from SD(n − 1) via a consecutive Noether gauge embedding procedure as shown in [19]. The equivalence among all those models can be proved by means of a master action approach [20]; see [19,21], which also furnishes a dual map e μν → e * μν responsible for the equivalence of correlation functions of e μν in the SD1 model with correlation functions of e * μν in the higher-order SDn models. All SDn models can be written in a compact way 3 like the first-order model of Aragone and Khoudeir [24], which was the first one to be suggested, namely…”

“…Consequently, the linearized K-term (NMG case) and the linearized gravitational Chern-Simons term (TMG case) still have one more local symmetry than the EH term, namely, they are invariant under longitudinal diffeomorphisms: δ h μν = ∂ μ ∂ ν ζ . Indeed, such symmetry can be used in order to obtain the WSD4 model, which is equivalent to SD4, from the WSD3 model via Noether gauge embedding just like the Weyl symmetry is used to get from SD3 to SD4 as shown in [19]. Therefore, the pure longitudinal sector of the metric will behave like 1/P 2 .…”

“…The case of HDTMG [19,26], i.e., the nonlinear completion of SD4, is even worse from the point of view of perturbative quantum field theory. Both terms of the quadratic (free) piece of HDTMG, i.e., the linearized K-term and the linearized gravitational Chern-Simons term are invariant under linearized WDIFF while the cubic and higher vertices are only invariant under DIFF.…”

Dual embedding of extended models with a Lorentz-breaking mass term

“…Alternatives to avoid the emergency of ghosts in the process of dualization were developed [39], [40], [41], [42]. In some approaches, the price to be paid is the lost of locality [39].…”