Spin-2 Fields  

In General > s.a. graviton; Pauli-Fierz Theory; theories of gravity; types of gauge theories.
* Remark: For a linear theory, consistency requires that a second-order field equation for a free massless rank-2, symmetric tensor field on some background be the linearized Einstein equation; On the other hand, non-linear generalizations of a spin-2 linear field theory can have different symmetry groups; When the fields are geometrized and the theory made diffeomorphism-invariant, one gets the non-linear dynamics of general relativity (or as the torsion of a Cartan geometry), or a higher-order theory; In other words, the only known fully ghost-free and consistent Lorentz-invariant kinetic term for a spin-2 field is the Einstein-Hilbert term (and the field is the graviton).
* Field equations: Described by a symmetric hab; In the massless case,

cc hab + ∂ab h − 2 ∂c(a hb) cηabcc h + ηabcd hcd = 0 .

@ General references: in Wentzel 49; van Nieuwenhuizen NPB(73) [and linearized general relativity]; Wald PRD(86) [and general covariance], CQG(87), in(88); Cutler & Wald CQG(87); Heiderich & Unruh PRD(88); Friedrich CQG(03) [near infinity]; in Franklin 10 [IIb]; Arcos et al CQG(10)-a1001 [as translation-Lie-algebra-valued vector field]; Arcos et al FP(12)-a1110 [helicity]; Folkerts et al a1107; Cirilo-Lombardo G&C-a1405 [Bronstein's work on quantization and wave equations]; Naruko et al PRD(19)-a1812 [Lorentz-invariant theories]; Jezierski et al a2004 [localized energy].
@ Interactions: Hinterbichler & Rosen JHEP(12)-a1203 [in arbitrary dimensions, without Boulware-Deser ghosts]; Mayor et al G&C(13) [conformally and gauge-invariant field equations]; Gao PRD(14)-a1403 [Lorentz-invariant derivative interactions]; Noller JCAP(15)-a1409 [consistent kinetic and derivative interactions]; de Rham et al CQG(15)-a1410 [for charged spin-2 fields]; Afshar et al JHEP(15)-a1410 [3D]; Hertzberg & Sandora JHEP(17)-a1702 [and causality].
@ Related topics: Buchbinder et al PLB(99)ht [in string theory]; Boulanger et al ht/00-proc [consistency]; Magnano & Sokołowski AP(03) [and higher-derivative]; Blas JPA(07)ht-in [without ghosts or tachyons]; Buchbinder et al PLB(10)-a0912 [BRST Lagrangian construction]; Ben Achour et al PRD(14)-a1311 [conformally-invariant wave equation, in d dimensions]; Noller et al JCAP(14)-a1311 [interacting, in the Stückelberg picture]; Hertzberg & Sandora PRD(17)-a1704 [theories of massless spin-2 and spin-1 particles, soft gravitons, and special relativity].

In Curved Spacetime > s.a. asymptotic flatness at null infinity; fields in schwarzschild spacetime.
@ General references: Bengtsson JMP(95)gq/94; Novello & Neves CQG(02)gq [Fierz representation]; Deser & Henneaux CQG(07)gq/06 [re consistency]; Papini PRD(07)gq; Zecca IJTP(09) [in FLRW spacetime]; Grisa & Sorbo PLB(10) [Pauli-Fierz gravitons in FLRW spacetime]; > s.a. schwarzschild and kerr spacetimes.
@ Using a non-symmetric tensor: Dalmazi et al PRD(17)-a1706, Mazuet & Volkov JCAP(18)-a1804 [massive]; Fortes & Dalmazi PRD(19)-a1901 [massless and partially massless].
@ In (A)dS spacetime: Deser & Waldron PLB(01), Polishchuk TMP(04) [massive, AdS]; Gabadadze et al a0809 [massive, de Sitter space]; Zinoviev MPLA(09) [massless, electromagnetic interactions]; Zinoviev NPB(09)-a0901 [massive, electromagnetic interactions].
@ Other cosmology: Tamanini et al JCAP(14)-a1307; Barceló et al PRD(14)-a1401, AP(18)-a1406 [graviton self-interactions and the cosmological constant]; Maia IJMPA(16)-a1509.
@ Coupled to gravity: Buchbinder et al NPB(00)ht/99 [coupled to gravity]; Hassan et al JHEP(13)-a1208 [massive]; Joung et al PRL(14)-a1406, García-Saenz et al JHEP(16)-a1511 [partially massless, no-go theorems].

Other Variations > s.a. bimetric theory.
@ General references: López-Pinto gq/04 [non-standard].
@ Massive: Zinoviev JHEP(05)ht [dual formulation], NPB(07) [possible interactions]; Folkerts et al CEJP-a1310 [and non-linear completion]; Hod CQG(13)-a1402 [late-time tails]; Ohara et al PRD(14)-a1402 [renormalizable theory]; Akagi et al PRD(14)-a1410 [in curved spacetime, with non-minimal coupling, ghost-free]; Nojiri a1411-proc [new ghost-free model]; Bonifacio et al PRD(15)-a1501 [TDiff and Weyl invariant]; Koenigstein et al AP(16)-a1508 [non-interacting, classical and quantum theory]; Ohara PRD(16)-a1606 [charged, self-interacting]; Akagi a1810 [in curved spacetime]; Curtright & Alshal NPB(19)-a1907 [massive dual spin-2 field theory]; Alberte et al JHEP(20)-a1910 [interacting massive spin-2 fields, effective field theory]; Dalmazi & dos Santos a2003 [dual actions].
@ In electromagnetic background: Klishevich & Zinoviev PAN(98)ht/97 [massive]; Novello et al ht/03 & ht/03, Deser & Waldron ht/03 [acausality].
@ And torsion: Novello gq/02; Nair et al PRD(09)-a0811 [massive, from torsion, in curved spacetime]; > s.a. schwarzschild spacetime.

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