ABSTRACT
We introduce a systematic way of constructing 3D exotic massive gravity theories in the first order formulation. Our method is based on truncating a single degree of freedom in the parity odd gravity models found earlier [1] and supplementing it with appropriate potential terms such that the resulting models have well-defined metric equations but their Bianchi identities are satisfied only on-shell. Hence, they are ‘third way’ consistent. We first re-derive two already known exotic theories using our approach and then construct an extended exotic massive gravity model whose metric field equation is sixth order in derivatives. We also explain how to check Bianchi identities using the first order formulation.
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H.R. Afshar, E.A. Bergshoeff and W. Merbis, Extended massive gravity in three dimensions, JHEP 08 (2014) 115 [arXiv:1405.6213] [INSPIRE].
W. Li, W. Song and A. Strominger, Chiral gravity in three dimensions, JHEP 04 (2008) 082 [arXiv:0801.4566] [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].
E.A. Bergshoeff, O. Hohm, W. Merbis, A.J. Routh and P.K. Townsend, Chern-Simons-like gravity theories, Lect. Notes Phys. 892 (2015) 181 [arXiv:1402.1688] [INSPIRE].
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].
S. Deser, R. Jackiw and S. Templeton, Topologically massive gauge theories, Annals Phys. 140 (1982) 372 [Erratum ibid. 185 (1988) 406] [Annals Phys. 281 (2000) 409] [INSPIRE].
J.H. Horne and E. Witten, Conformal gravity in three-dimensions as a gauge theory, Phys. Rev. Lett. 62 (1989) 501 [INSPIRE].
H. Afshar, B. Cvetkovic, S. Ertl, D. Grumiller and N. Johansson, Conformal Chern-Simons holography — lock, stock and barrel, Phys. Rev. D 85 (2012) 064033 [arXiv:1110.5644] [INSPIRE].
H.R. Afshar, Flat/AdS boundary conditions in three dimensional conformal gravity, JHEP 10 (2013) 027 [arXiv:1307.4855] [INSPIRE].
E. Bergshoeff, O. Hohm, W. Merbis, A.J. Routh and P.K. Townsend, Minimal massive 3D gravity, Class. Quant. Grav. 31 (2014) 145008 [arXiv:1404.2867] [INSPIRE].
A.S. Arvanitakis and P.K. Townsend, Minimal massive 3D gravity unitarity redux, Class. Quant. Grav. 32 (2015) 085003 [arXiv:1411.1970] [INSPIRE].
A.S. Arvanitakis, A. Sevrin and P.K. Townsend, Yang-Mills as massive Chern-Simons theory: a third way to three-dimensional gauge theories, Phys. Rev. Lett. 114 (2015) 181603 [arXiv:1501.07548] [INSPIRE].
E. Bergshoeff, W. Merbis, A.J. Routh and P.K. Townsend, The third way to 3D gravity, Int. J. Mod. Phys. D 24 (2015) 1544015 [arXiv:1506.05949] [INSPIRE].
M. Özkan, Y. Pang and P.K. Townsend, Exotic massive 3D gravity, JHEP 08 (2018) 035 [arXiv:1806.04179] [INSPIRE].
G. Alkaç, M. Tek and B. Tekin, Bachian gravity in three dimensions, Phys. Rev. D 98 (2018) 104021 [arXiv:1810.03504] [INSPIRE].
E. Witten, (2 + 1)-dimensional gravity as an exactly soluble system, Nucl. Phys. B 311 (1988) 46 [INSPIRE].
E.A. Bergshoeff, S. de Haan, O. Hohm, W. Merbis and P.K. Townsend, Zwei-Dreibein gravity: a two-frame-field model of 3D massive gravity, Phys. Rev. Lett. 111 (2013) 111102 [Erratum ibid. 111 (2013) 259902] [arXiv:1307.2774] [INSPIRE].
H.R. Afshar, E.A. Bergshoeff and W. Merbis, Interacting spin-2 fields in three dimensions, JHEP 01 (2015) 040 [arXiv:1410.6164] [INSPIRE].
I. Gullu, T.C. Sisman and B. Tekin, Born-Infeld extension of new massive gravity, Class. Quant. Grav. 27 (2010) 162001 [arXiv:1003.3935] [INSPIRE].
A. Achucarro and P.K. Townsend, A Chern-Simons action for three-dimensional anti-de Sitter supergravity theories, Phys. Lett. B 180 (1986) 89 [INSPIRE].
P.K. Townsend and B. Zhang, Thermodynamics of “exotic” Bañados-Teitelboim-Zanelli black holes, Phys. Rev. Lett. 110 (2013) 241302 [arXiv:1302.3874] [INSPIRE].
M. Ozkan, Y. Pang and U. Zorba, Unitary extension of exotic massive 3D gravity from bigravity, Phys. Rev. Lett. 123 (2019) 031303 [arXiv:1905.00438] [INSPIRE].
A.S. Arvanitakis, A.J. Routh and P.K. Townsend, Matter coupling in 3D ‘minimal massive gravity’, Class. Quant. Grav. 31 (2014) 235012 [arXiv:1407.1264] [INSPIRE].
G. Alkac, L. Basanisi, E. Kilicarslan and B. Tekin, Unitarity problems in 3D gravity theories, Phys. Rev. D 96 (2017) 024010 [arXiv:1703.03630] [INSPIRE].
M. Chernicoff, G. Giribet, N. Grandi and J. Oliva, Vacua of exotic massive 3D gravity, JHEP 08 (2018) 087 [arXiv:1806.06254] [INSPIRE].
G. Giribet and J. Oliva, More on vacua of exotic massive 3D gravity, Phys. Rev. D 99 (2019) 064021 [arXiv:1901.08457] [INSPIRE].
R.B. Mann, J. Oliva and S.N. Sajadi, Energy of asymptotically AdS black holes in exotic massive gravity and its log-extension, JHEP 05 (2019) 131 [arXiv:1812.09525] [INSPIRE].
E. Kilicarslan and B. Tekin, Exotic massive gravity: causality and a Birkhoff-like theorem, Phys. Rev. D 100 (2019) 044035 [arXiv:1906.09429] [INSPIRE].
H. Adami, M.R. Setare, T.C. Sisman and B. Tekin, Conserved charges in extended theories of gravity, arXiv:1710.07252 [INSPIRE].
B. Tekin, Minimal massive gravity: conserved charges, excitations and the chiral gravity limit, Phys. Rev. D 90 (2014) 081701 [arXiv:1409.5358] [INSPIRE].
E.A. Bergshoeff, W. Merbis and P.K. Townsend, On-shell versus off-shell equivalence in 3D gravity, Class. Quant. Grav. 36 (2019) 095013 [arXiv:1812.09205] [INSPIRE].
E.A. Bergshoeff, W. Merbis and P.K. Townsend, On asymptotic charges in 3D gravity, arXiv:1909.11743 [INSPIRE].
M.-I. Park, Thermodynamics of exotic black holes, negative temperature and Bekenstein-Hawking entropy, Phys. Lett. B 647 (2007) 472 [hep-th/0602114] [INSPIRE].
M. Geiller and K. Noui, A remarkably simple theory of 3d massive gravity, JHEP 04 (2019) 091 [arXiv:1812.01018] [INSPIRE].
M. Geiller and K. Noui, Metric formulation of the simple theory of 3d massive gravity, Phys. Rev. D 100 (2019) 064066 [arXiv:1905.04390] [INSPIRE].
D. Grumiller, W. Riedler, J. Rosseel and T. Zojer, Holographic applications of logarithmic conformal field theories, J. Phys. A 46 (2013) 494002 [arXiv:1302.0280] [INSPIRE].
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Afshar, H.R., Deger, N.S. Exotic massive 3D gravities from truncation. J. High Energ. Phys. 2019, 145 (2019). https://doi.org/10.1007/JHEP11(2019)145
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DOI: https://doi.org/10.1007/JHEP11(2019)145