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\( \mathcal{N} =2 \) \( \mathrm{AdS}_4\) supergravity, holography and Ward identities. (English) Zbl 1460.83108
Summary: We develop in detail the holographic framework for an \(\mathcal{N} = 2\) pure AdS supergravity model in four dimensions, including all the contributions from the fermionic fields and adopting the Fefferman-Graham parametrization. We work in the first order formalism, where the full superconformal structure can be kept manifest in principle, even if only a part of it is realized as a symmetry on the boundary, while the remainder has a non-linear realization. Our study generalizes the results presented in antecedent literature and includes a general discussion of the gauge-fixing conditions on the bulk fields which yield the asymptotic symmetries at the boundary. We construct the corresponding superconformal currents and show that they satisfy the related Ward identities when the bulk equations of motion are imposed. Consistency of the holographic setup requires the super-AdS curvatures to vanish at the boundary. This determines, in particular, the expression of the super-Schouten tensor of the boundary theory, which generalizes the purely bosonic Schouten tensor of standard gravity by including gravitini bilinears. The same applies to the superpartner of the super-Schouten tensor, the conformino. Furthermore, the vanishing of the supertorsion poses general constraints on the sources of the three-dimensional boundary conformal field theory and requires that the super-Schouten tensor is endowed with an antisymmetric part proportional to a gravitino-squared term.
MSC:
83E50 Supergravity
83E05 Geometrodynamics and the holographic principle
83C45 Quantization of the gravitational field
81R15 Operator algebra methods applied to problems in quantum theory
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References:
[1] Maldacena, JM, The Large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys., 38, 1113 (1999) · Zbl 0969.81047
[2] Gubser, SS; Klebanov, IR; Polyakov, AM, Gauge theory correlators from noncritical string theory, Phys. Lett. B, 428, 105 (1998) · Zbl 1355.81126
[3] Witten, E., Anti-de Sitter space and holography, Adv. Theor. Math. Phys., 2, 253 (1998) · Zbl 0914.53048
[4] Skenderis, K., Lecture notes on holographic renormalization, Class. Quant. Grav., 19, 5849 (2002) · Zbl 1044.83009
[5] O. DeWolfe, TASI Lectures on Applications of Gauge/Gravity Duality, PoSTASI2017 (2018) 014 [arXiv:1802.08267] [INSPIRE].
[6] A.J. Amsel and G. Compere, Supergravity at the boundary of AdS supergravity, Phys. Rev. D79 (2009) 085006 [arXiv:0901.3609] [INSPIRE].
[7] Papadimitriou, I., Supercurrent anomalies in 4d SCFTs, JHEP, 07, 038 (2017) · Zbl 1380.81354
[8] Henningson, M.; Skenderis, K., The Holographic Weyl anomaly, JHEP, 07, 023 (1998) · Zbl 0958.81083
[9] S. de Haro, S.N. Solodukhin and K. Skenderis, Holographic reconstruction of space-time and renormalization in the AdS/CFT correspondence, Commun. Math. Phys.217 (2001) 595 [hep-th/0002230] [INSPIRE]. · Zbl 0984.83043
[10] Bianchi, M.; Freedman, DZ; Skenderis, K., Holographic renormalization, Nucl. Phys. B, 631, 159 (2002) · Zbl 0995.81075
[11] Gibbons, GW; Hawking, SW, Action Integrals and Partition Functions in Quantum Gravity, Phys. Rev. D, 15, 2752 (1977)
[12] J.D. Brown and J.W. York Jr., Quasilocal energy and conserved charges derived from the gravitational action, Phys. Rev. D47 (1993) 1407 [gr-qc/9209012] [INSPIRE].
[13] An, OS, Anomaly-corrected supersymmetry algebra and supersymmetric holographic renormalization, JHEP, 12, 107 (2017) · Zbl 1383.81174
[14] Mišković, O.; Olea, R., Topological regularization and self-duality in four-dimensional anti-de Sitter gravity, Phys. Rev. D, 79, 124020 (2009)
[15] Anastasiou, G.; Mišković, O.; Olea, R.; Papadimitriou, I., Counterterms, Kounterterms, and the variational problem in AdS gravity, JHEP, 08, 061 (2020) · Zbl 1454.83007
[16] R. Aros, M. Contreras, R. Olea, R. Troncoso and J. Zanelli, Conserved charges for gravity with locally AdS asymptotics, Phys. Rev. Lett.84 (2000) 1647 [gr-qc/9909015] [INSPIRE].
[17] R. Aros, M. Contreras, R. Olea, R. Troncoso and J. Zanelli, Conserved charges for even dimensional asymptotically AdS gravity theories, Phys. Rev. D62 (2000) 044002 [hep-th/9912045] [INSPIRE].
[18] Olea, R., Mass, angular momentum and thermodynamics in four-dimensional Kerr-AdS black holes, JHEP, 06, 023 (2005)
[19] S.W. MacDowell and F. Mansouri, Unified Geometric Theory of Gravity and Supergravity, Phys. Rev. Lett.38 (1977) 739 [Erratum ibid.38 (1977) 1376] [INSPIRE].
[20] Korovin, Y.; Kuzenko, SM; Theisen, S., The conformal supercurrents in diverse dimensions and conserved superconformal currents, JHEP, 05, 134 (2016) · Zbl 1388.81679
[21] Korovin, Y., Asymptotic symmetries and geometry on the boundary in the first order formalism, JHEP, 03, 017 (2018) · Zbl 1388.81678
[22] Bañados, M.; Mišković, O.; Theisen, S., Holographic currents in first order gravity and finite Fefferman-Graham expansions, JHEP, 06, 025 (2006)
[23] D. Klemm and G. Tagliabue, The CFT dual of AdS gravity with torsion, Class. Quant. Grav.25 (2008) 035011 [arXiv:0705.3320] [INSPIRE]. · Zbl 1136.83034
[24] Blagojevic, M.; Cvetkovic, B.; Mišković, O.; Olea, R., Holography in 3D AdS gravity with torsion, JHEP, 05, 103 (2013) · Zbl 1342.83335
[25] A.C. Petkou, Torsional degrees of freedom in AdS_4/CFT_3, arXiv:1004.1640 [INSPIRE].
[26] L. Ciambelli and R.G. Leigh, Weyl Connections and their Role in Holography, Phys. Rev. D101 (2020) 086020 [arXiv:1905.04339] [INSPIRE].
[27] Andrianopoli, L.; D’Auria, R., N = 1 and N = 2 pure supergravities on a manifold with boundary, JHEP, 08, 012 (2014)
[28] Álvarez, PD; Valenzuela, M.; Zanelli, J., Supersymmetry of a different kind, JHEP, 04, 058 (2012) · Zbl 1348.81394
[29] Andrianopoli, L.; Cerchiai, BL; D’Auria, R.; Trigiante, M., Unconventional supersymmetry at the boundary of AdS4 supergravity, JHEP, 04, 007 (2018) · Zbl 1390.83359
[30] L. Andrianopoli et al., \( \mathcal{N} \)-extended D = 4 supergravity, unconventional SUSY and graphene, JHEP01 (2020) 084 [arXiv:1910.03508] [INSPIRE]. · Zbl 1434.83153
[31] Andrianopoli, L.; Cerchiai, BL; Grassi, PA; Trigiante, M., The Quantum Theory of Chern-Simons Supergravity, JHEP, 06, 036 (2019) · Zbl 1416.83133
[32] Gaiotto, D.; Witten, E., Janus Configurations, Chern-Simons Couplings, And The theta-Angle in N = 4 Super Yang-Mills Theory, JHEP, 06, 097 (2010) · Zbl 1290.81065
[33] Brown, JD; Henneaux, M., Central Charges in the Canonical Realization of Asymptotic Symmetries: An Example from Three-Dimensional Gravity, Commun. Math. Phys., 104, 207 (1986) · Zbl 0584.53039
[34] Henneaux, M.; Teitelboim, C., Asymptotically anti-de Sitter Spaces, Commun. Math. Phys., 98, 391 (1985) · Zbl 1032.83502
[35] Imbimbo, C.; Schwimmer, A.; Theisen, S.; Yankielowicz, S., Diffeomorphisms and holographic anomalies, Class. Quant. Grav., 17, 1129 (2000) · Zbl 0952.81052
[36] R.L. Arnowitt, S. Deser and C.W. Misner, The Dynamics of general relativity, Gen. Rel. Grav.40 (2008) 1997 [gr-qc/0405109] [INSPIRE]. · Zbl 1152.83320
[37] S. de Haro, Dual Gravitons in AdS_4/CFT_3and the Holographic Cotton Tensor, JHEP01 (2009) 042 [arXiv:0808.2054] [INSPIRE]. · Zbl 1243.83068
[38] A. Garcia, F.W. Hehl, C. Heinicke and A. Macias, The Cotton tensor in Riemannian space-times, Class. Quant. Grav.21 (2004) 1099 [gr-qc/0309008] [INSPIRE]. · Zbl 1045.83051
[39] L. Castellani, R. D’Auria and P. Fre, Supergravity and superstrings: A Geometric perspective. Vol. 1: Mathematical foundations, World Scientific, Singapore (1991) [INSPIRE]. · Zbl 0753.53047
[40] L. Castellani, R. D’Auria and P. Fre, Supergravity and superstrings: A Geometric perspective. Vol. 2: Supergravity, World Scientific, Singapore (1991) [INSPIRE]. · Zbl 0753.53047
[41] R. D’Auria, Geometric supergravitty, arXiv:2005.13593 [INSPIRE].
[42] Castellani, L.; Catenacci, R.; Grassi, PA, Supergravity Actions with Integral Forms, Nucl. Phys. B, 889, 419 (2014) · Zbl 1326.81200
[43] Castellani, L.; Catenacci, R.; Grassi, PA, The Geometry of Supermanifolds and New Supersymmetric Actions, Nucl. Phys. B, 899, 112 (2015) · Zbl 1331.81271
[44] L. Andrianopoli et al., N = 2 supergravity and N = 2 superYang-Mills theory on general scalar manifolds: Symplectic covariance, gaugings and the momentum map, J. Geom. Phys.23 (1997) 111 [hep-th/9605032] [INSPIRE]. · Zbl 0899.53073
[45] York, JW Jr, Role of conformal three geometry in the dynamics of gravitation, Phys. Rev. Lett., 28, 1082 (1972)
[46] Papadimitriou, I.; Skenderis, K., Thermodynamics of asymptotically locally AdS spacetimes, JHEP, 08, 004 (2005)
[47] Kraus, P.; Larsen, F.; Siebelink, R., The gravitational action in asymptotically AdS and flat space-times, Nucl. Phys. B, 563, 259 (1999) · Zbl 0953.83040
[48] Myers, RC, Higher Derivative Gravity, Surface Terms and String Theory, Phys. Rev. D, 36, 392 (1987)
[49] Emparan, R.; Johnson, CV; Myers, RC, Surface terms as counterterms in the AdS/CFT correspondence, Phys. Rev. D, 60, 104001 (1999)
[50] Balasubramanian, V.; Kraus, P., A Stress tensor for Anti-de Sitter gravity, Commun. Math. Phys., 208, 413 (1999) · Zbl 0946.83013
[51] Katsianis, G.; Papadimitriou, I.; Skenderis, K.; Taylor, M., Anomalous Supersymmetry, Phys. Rev. Lett., 122, 231602 (2019)
[52] Papadimitriou, I., Supersymmetry anomalies in \(\mathcal{N} = 1\) conformal supergravity, JHEP, 04, 040 (2019) · Zbl 1415.83070
[53] Anastasiou, G.; Araya, IJ; Arias, C.; Olea, R., Einstein-AdS action, renormalized volume/area and holographic Rényi entropies, JHEP, 08, 136 (2018) · Zbl 1396.83004
[54] Fradkin, ES; Tseytlin, AA, Conformal supergravity, Phys. Rept., 119, 233 (1985)
[55] Howe, PS; Izquierdo, JM; Papadopoulos, G.; Townsend, PK, New supergravities with central charges and Killing spinors in (2 + 1)-dimensions, Nucl. Phys. B, 467, 183 (1996) · Zbl 1003.83518
[56] Butter, D.; Kuzenko, SM; Novak, J.; Tartaglino-Mazzucchelli, G., Conformal supergravity in three dimensions: New off-shell formulation, JHEP, 09, 072 (2013) · Zbl 1342.83452
[57] Castellani, L.; Ceresole, A.; D’Auria, R.; Ferrara, S.; Fré, P.; Trigiante, M., G/H M-branes and AdS_p+2geometries, Nucl. Phys. B, 527, 142 (1998) · Zbl 0956.83058
[58] Dall’Agata, G.; Fabbri, D.; Fraser, C.; Fré, P.; Termonia, P.; Trigiante, M., The Osp(8||4) singleton action from the supermembrane, Nucl. Phys. B, 542, 157 (1999) · Zbl 0942.81059
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