Abstract
A procedure to obtain higher-derivative free massive actions is proposed. It consists in dimensional reduction of conventional two-derivative massless actions, where solutions to constraints bring in higher derivatives. We apply this procedure to derive the arbitrary dimensional generalizations of (linearized) New Massive Gravity and New Topologically Massive Gravity.
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E.A. Bergshoeff, O. Hohm and P.K. Townsend, Massive gravity in three dimensions, Phys. Rev. Lett. 102 (2009) 201301 [arXiv:0901.1766] [INSPIRE].
E.A. Bergshoeff, O. Hohm and P.K. Townsend, More on massive 3D gravity, Phys. Rev. D 79 (2009) 124042 [arXiv:0905.1259] [INSPIRE].
E.A. Bergshoeff, J. Fernandez-Melgarejo, J. Rosseel and P.K. Townsend, On ’new massive’ 4D gravity, JHEP 04 (2012) 070 [arXiv:1202.1501] [INSPIRE].
K. Morand and S.N. Solodukhin, Dual massive gravity, Phys. Lett. B 715 (2012) 260 [arXiv:1204.6224] [INSPIRE].
S. Deser, R. Jackiw and S. Templeton, Topologically massive gauge theories, Annals Phys. 140 (1982) 372 [Erratum ibid. 185 (1988) 406] [INSPIRE].
R. Andringa et al., Massive 3D supergravity, Class. Quant. Grav. 27 (2010) 025010 [arXiv:0907.4658] [INSPIRE].
D. Dalmazi and E. Mendonca, A new spin-2 self-dual model in D = 2 + 1, JHEP 09 (2009) 011 [arXiv:0907.5009] [INSPIRE].
E.A. Bergshoeff, M. Kovacevic, J. Rosseel and Y. Yin, On topologically massive spin-2 gauge theories beyond three dimensions, JHEP 10 (2012) 055 [arXiv:1207.0192] [INSPIRE].
T. Damour and S. Deser, ’Geometry’ of spin 3 gauge theories, Annales Poincaré Phys. Theor. 47 (1987) 277 [INSPIRE].
S. Deser, Ghost-free, finite, fourth order D = 3 (alas) gravity, Phys. Rev. Lett. 103 (2009) 101302 [arXiv:0904.4473] [INSPIRE].
E.A. Bergshoeff, O. Hohm and P.K. Townsend, On higher derivatives in 3D gravity and higher spin gauge theories, Annals Phys. 325 (2010) 1118 [arXiv:0911.3061] [INSPIRE].
I. Gullu, T.C. Sisman and B. Tekin, Canonical structure of higher derivative gravity in 3D, Phys. Rev. D 81 (2010) 104017 [arXiv:1002.3778] [INSPIRE].
E.A. Bergshoeff, M. Kovacevic, J. Rosseel, P.K. Townsend and Y. Yin, A spin-4 analog of 3D massive gravity, Class. Quant. Grav. 28 (2011) 245007 [arXiv:1109.0382] [INSPIRE].
N. Ohta, A complete classification of higher derivative gravity in 3D and criticality in 4D, Class. Quant. Grav. 29 (2012) 015002 [arXiv:1109.4458] [INSPIRE].
O. Hohm, A. Routh, P.K. Townsend and B. Zhang, On the Hamiltonian form of 3D massive gravity, Phys. Rev. D 86 (2012) 084035 [arXiv:1208.0038] [INSPIRE].
X. Bekaert and M. Henneaux, Comments on chiral p forms, Int. J. Theor. Phys. 38 (1999) 1161 [hep-th/9806062] [INSPIRE].
M. Henneaux and C. Teitelboim, Duality in linearized gravity, Phys. Rev. D 71 (2005) 024018 [gr-qc/0408101] [INSPIRE].
M. Dubois-Violette and M. Henneaux, Generalized cohomology for irreducible tensor fields of mixed Young symmetry type, Lett. Math. Phys. 49 (1999) 245 [math/9907135] [INSPIRE].
M. Dubois-Violette and M. Henneaux, Tensor fields of mixed Young symmetry type and N complexes, Commun. Math. Phys. 226 (2002) 393 [math/0110088] [INSPIRE].
X. Bekaert and N. Boulanger, Tensor gauge fields in arbitrary representations of GL(D, R): Duality and Poincaré lemma, Commun. Math. Phys. 245 (2004) 27 [hep-th/0208058] [INSPIRE].
T. Curtright, Generalized gauge fields, Phys. Lett. B 165 (1985) 304 [INSPIRE].
P. Townsend, K. Pilch and P. van Nieuwenhuizen, Selfduality in odd dimensions, Phys. Lett. B 136 (1984) 38 [Addendum ibid. B 137 (1984) 443] [INSPIRE].
S. Deser and R. Jackiw, ’Selfduality’ of topologically massive gauge theories, Phys. Lett. B 139 (1984) 371 [INSPIRE].
C. Aragone and A. Khoudeir, Selfdual massive gravity, Phys. Lett. B 173 (1986) 141 [INSPIRE].
S. Deser and J.G. McCarthy, Selfdual formulations of D = 3 gravity theories, Phys. Lett. B 246 (1990) 441 [Addendum ibid. B 248 (1990) 473] [INSPIRE].
I. Tyutin and M.A. Vasiliev, Lagrangian formulation of irreducible massive fields of arbitrary spin in (2 + 1)-dimensions, Teor. Mat. Fiz. 113N1 (1997) 45 [hep-th/9704132] [INSPIRE].
S. Carlip, S. Deser, A. Waldron and D. Wise, Cosmological topologically massive gravitons and photons, Class. Quant. Grav. 26 (2009) 075008 [arXiv:0803.3998] [INSPIRE].
D. Dalmazi and E.L. Mendonca, Dual descriptions of spin two massive particles in D = 2 + 1 via master actions, Phys. Rev. D 79 (2009) 045025 [arXiv:0812.0161] [INSPIRE].
D. Dalmazi and E.L. Mendonca, Duality of parity doublets of helicity ± 2 in D = 2 + 1, Phys. Rev. D 82 (2010) 105009 [arXiv:1008.2476] [INSPIRE].
B. Chen, J. Long and J.-B. Wu, Spin-3 topological massive gravity, Phys. Lett. B 705 (2011) 513 [arXiv:1106.5141] [INSPIRE].
A. Bagchi, S. Lal, A. Saha and B. Sahoo, Topologically massive higher spin gravity, JHEP 10 (2011) 150 [arXiv:1107.0915] [INSPIRE].
A. Bagchi, S. Lal, A. Saha and B. Sahoo, One loop partition function for topologically massive higher spin gravity, JHEP 12 (2011) 068 [arXiv:1107.2063] [INSPIRE].
B. Chen and J. Long, High spin topologically massive gravity, JHEP 12 (2011) 114 [arXiv:1110.5113] [INSPIRE].
P.J. Arias, A. Khoudeir and J. Stephany, Master actions for linearized massive gravity models in 3D, Int. J. Mod. Phys. A 27 (2012) 1250015 [Erratum ibid. A 27 (2012) 1292002] [arXiv:1201.2927] [INSPIRE].
S. Dengiz, E. Kilicarslan and B. Tekin, Weyl-gauging of topologically massive gravity, Phys. Rev. D 86 (2012) 104014 [arXiv:1209.1251] [INSPIRE].
M. Henneaux and C. Teitelboim, Dynamics of chiral (selfdual) p forms, Phys. Lett. B 206 (1988) 650 [INSPIRE].
E. Joung and K. Mkrtchyan, A note on higher-derivative actions for free higher-spin fields, JHEP 11 (2012) 153 [arXiv:1209.4864] [INSPIRE].
D. Francia, Generalised connections and higher-spin equations, Class. Quant. Grav. 29 (2012) 245003 [arXiv:1209.4885] [INSPIRE].
V. Ogievetsky and I. Polubarinov, The notoph and its possible interactions, Sov. J. Nucl. Phys. 4 (1967) 156 [INSPIRE].
S. Deser, P. Townsend and W. Siegel, Higher rank representations of lower spin, Nucl. Phys. B 184 (1981) 333 [INSPIRE].
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ArXiv ePrint: 1212.5919
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Joung, E., Mkrtchyan, K. Higher-derivative massive actions from dimensional reduction. J. High Energ. Phys. 2013, 134 (2013). https://doi.org/10.1007/JHEP02(2013)134
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DOI: https://doi.org/10.1007/JHEP02(2013)134