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

Autor: Denis Dalmazi, A. L. R. dos Santos, Subir Ghosh, E. L. Mendonça
Jazyk: angličtina
Rok vydání: 2017
Předmět:
Zdroj: European Physical Journal C: Particles and Fields, Vol 77, Iss 9, Pp 1-10 (2017)
Druh dokumentu: article
ISSN: 1434-6044
1434-6052
DOI: 10.1140/epjc/s10052-017-5189-7
Popis: Abstract There are two covariant descriptions of massless spin-2 particles in $$D=3+1$$ D = 3 + 1 via a symmetric rank-2 tensor: the linearized Einstein–Hilbert (LEH) theory and the Weyl plus transverse diffeomorphism (WTDIFF) invariant model. From the LEH theory one can obtain the linearized new massive gravity (NMG) in $$D=2+1$$ D = 2 + 1 via Kaluza–Klein dimensional reduction followed by a dual master action. Here we show that a similar route takes us from the WTDIFF model to a linearized scalar–tensor NMG which belongs to a larger class of consistent spin-0 modifications of NMG. We also show that a traceless master action applied to a parity singlet furnishes two new spin-2 self-dual models. Moreover, we examine the singular replacement $$h_{\mu \nu } \rightarrow h_{\mu \nu } - \eta _{\mu \nu }h/D$$ h μ ν → h μ ν - η μ ν h / D and prove that it leads to consistent massive spin-2 models in $$D=2+1$$ D = 2 + 1 . They include linearized versions of unimodular topologically massive gravity (TMG) and unimodular NMG. Although the free part of those unimodular theories are Weyl invariant, we do not expect any improvement in the renormalizability. Both the linearized K-term (in NMG) and the linearized gravitational Chern–Simons term (in TMG) are invariant under longitudinal reparametrizations $$\delta h_{\mu \nu } = \partial _{\mu }\partial _{\nu }\zeta $$ δ h μ ν = ∂ μ ∂ ν ζ , which is not a symmetry of the WTDIFF Einstein–Hilbert term. Therefore, we still have one degree of freedom whose propagator behaves like $$1/p^2$$ 1 / p 2 for large momentum.
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