Abstract
Basic aspects of the AdS/CFT correspondence are studied in the framework of 3-dimensional gravity with torsion. After choosing a consistent holographic ansatz, we formulate an improved approach to the Noether-Ward identities for the boundary theory. The method is applied first to the topological Mielke-Baekler model, and then to the more interesting (parity-preserving) 3-dimensional gravity with propagating torsion. In both cases, we find the finite holographic energy-momentum and spin currents and obtain the associated (anomalous) Noether-Ward identities.
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E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri and Y. Oz, Large-N field theories, string theory and gravity, Phys. Rept. 323 (2000) 183 [hep-th/9905111] [INSPIRE].
R. Bousso, The holographic principle, Rev. Mod. Phys. 74 (2002) 825 [hep-th/0203101] [INSPIRE].
M. Blagojević, Gravitation and gauge symmetries, IoP Publishing, Bristol U.K. (2002).
T. Ortín, Gravity and strings, Cambridge University Press, Cambridge U.K. (2004).
M. Blagojević and F.W. Hehl, Gauge theories of gravitation — a reader with commentaries, Imperial College Press, London U.K. (2013).
M. Bañados, O. Mišković and S. Theisen, Holographic currents in first order gravity and finite Fefferman-Graham expansions, JHEP 06 (2006) 025 [hep-th/0604148] [INSPIRE].
D. Klemm and G. Tagliabue, The CFT dual of AdS gravity with torsion, Class. Quant. Grav. 25 (2008) 035011 [arXiv:0705.3320] [INSPIRE].
E.W. Mielke and P. Baekler, Topological gauge model of gravity with torsion, Phys. Lett. A 156 (1991) 399 [INSPIRE].
A.C. Petkou, Torsional degrees of freedom in AdS 4 /CFT 3, arXiv:1004.1640 [INSPIRE].
M. Blagojević and B. Cvetković, Canonical structure of 3D gravity with torsion, in Progress in general relativity and quantum cosmology, volume 2, C. Benton ed., Nova Science Publishers, New York U.S.A. (2006), pg. 103 [gr-qc/0412134] [INSPIRE].
M. Blagojević and B. Cvetković, 3D gravity with propagating torsion: the AdS sector, Phys. Rev. D 85 (2012) 104003 [arXiv:1201.4277] [INSPIRE].
J. Helayël-Neto, C. Hernaski, B. Pereira-Dias, A. Vargas-Paredes and V. Vasquez-Otoya, Chern-Simons gravity with (curvature) 2 - and (torsion) 2 -terms and a basis of degree-of-freedom projection operators, Phys. Rev. D 82 (2010) 064014 [arXiv:1005.3831] [INSPIRE].
S. Deser, R. Jackiw and S. Templeton, Three-dimensional massive gauge theories, Phys. Rev. Lett. 48 (1982) 975 [INSPIRE].
S. Deser, R. Jackiw and S. Templeton, Topologically massive gauge theories, Annals Phys. 140 (1982) 372 [Erratum ibid. 185 (1988) 406] [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].
P.A. Dirac, Forms of relativistic dynamics, Rev. Mod. Phys. 21 (1949) 392 [INSPIRE].
C. Fefferman and R. Graham, Conformal invariants, in The mathematical heritage of Elie Cartan, Astérisque Numero Hors Serie 95, France (1985).
K. Skenderis, M. Taylor and B.C. van Rees, Topologically massive gravity and the AdS/CFT correspondence, JHEP 09 (2009) 045 [arXiv:0906.4926] [INSPIRE].
J.D. Brown and M. Henneaux, Central charges in the canonical realization of asymptotic symmetries: an example from three-dimensional gravity, Commun. Math. Phys. 104 (1986) 207 [INSPIRE].
M. Blagojević and B. Cvetković, Canonical structure of topologically massive gravity with a cosmological constant, JHEP 05 (2009) 073 [arXiv:0812.4742] [INSPIRE].
K. Skenderis and S.N. Solodukhin, Quantum effective action from the AdS/CFT correspondence, Phys. Lett. B 472 (2000) 316 [hep-th/9910023] [INSPIRE].
M. Bañados and F. Méndez, A note on covariant action integrals in three-dimensions, Phys. Rev. D 58 (1998) 104014 [hep-th/9806065] [INSPIRE].
O. Mišković and R. Olea, On boundary conditions in three-dimensional AdS gravity, Phys. Lett. B 640 (2006) 101 [hep-th/0603092] [INSPIRE].
R. Olea, Regularization of odd-dimensional AdS gravity: kounterterms, JHEP 04 (2007) 073 [hep-th/0610230] [INSPIRE].
V. Balasubramanian and P. Kraus, A stress tensor for anti-de Sitter gravity, Commun. Math. Phys. 208 (1999) 413 [hep-th/9902121] [INSPIRE].
G. Giribet and M. Leston, Boundary stress tensor and counterterms for weakened AdS 3 asymptotic in new massive gravity, JHEP 09 (2010) 070 [arXiv:1006.3349] [INSPIRE].
G. Giribet, J. Oliva, D. Tempo and R. Troncoso, Microscopic entropy of the three-dimensional rotating black hole of BHT massive gravity, Phys. Rev. D 80 (2009) 124046 [arXiv:0909.2564] [INSPIRE].
S. Deser and A. Schwimmer, Geometric classification of conformal anomalies in arbitrary dimensions, Phys. Lett. B 309 (1993) 279 [hep-th/9302047] [INSPIRE].
H. Nieh and M. Yan, An identity in Riemann-Cartan geometry, J. Math. Phys. 23 (1982) 373 [INSPIRE].
H. Nieh and C. Yang, A torsional topological invariant, Int. J. Mod. Phys. A 22 (2007) 5237 [INSPIRE].
S. Deser et al., Critical points of D-dimensional extended gravities, Phys. Rev. D 83 (2011) 061502 [arXiv:1101.4009] [INSPIRE].
C. Imbimbo, A. Schwimmer, S. Theisen and S. Yankielowicz, Diffeomorphisms and holographic anomalies, Class. Quant. Grav. 17 (2000) 1129 [hep-th/9910267] [INSPIRE].
A. Schwimmer and S. Theisen, Universal features of holographic anomalies, JHEP 10 (2003) 001 [hep-th/0309064] [INSPIRE].
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ArXiv ePrint: 1301.1237
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Blagojević, M., Cvetković, B., Miskovic, O. et al. Holography in 3D AdS gravity with torsion. J. High Energ. Phys. 2013, 103 (2013). https://doi.org/10.1007/JHEP05(2013)103
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DOI: https://doi.org/10.1007/JHEP05(2013)103