Abstract
A systematic off-shell reduction scheme from five to four space-time dimensions is presented for supergravity theories with eight supercharges. It is applicable to theories with higher-derivative couplings and it is used to address a number of open questions regarding BPS black holes in five dimensions. Under this reduction the 5D Weyl multiplet becomes reducible and decomposes into the 4D Weyl multiplet and an extra Kaluza-Klein vector multiplet. The emergence of the pseudoscalar field of the latter multiplet and the emergence of the 4D R-symmetry group are subtle features of the reduction. The reduction scheme enables to determine how a 5D supersymmetric Lagrangian with higher-derivative couplings decomposes upon dimensional reduction into a variety of independent 4D supersymmetric invariants, without the need for imposing field equations. In this way we establish, for example, the existence of a new N=2 supersymmetric invariant that involves the square of the Ricci tensor. Finally we resolve the questions associated with the 5D Chern-Simons terms for spinning BPS black holes and their relation to the corresponding 4D black holes.
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References
B. de Wit, F. Vanderseypen and A. Van Proeyen, Symmetry structure of special geometries, Nucl. Phys. B 400 (1993) 463 [hep-th/9210068] [INSPIRE].
D. Gaiotto, A. Strominger and X. Yin, New connections between 4D and 5D black holes, JHEP 02 (2006) 024 [hep-th/0503217] [INSPIRE].
D. Gaiotto, A. Strominger and X. Yin, 5D black rings and 4D black holes, JHEP 02 (2006) 023 [hep-th/0504126] [INSPIRE].
K. Behrndt, G. Lopes Cardoso and S. Mahapatra, Exploring the relation between 4D and 5D BPS solutions, Nucl. Phys. B 732 (2006) 200 [hep-th/0506251] [INSPIRE].
T. Kugo and K. Ohashi, Supergravity tensor calculus in 5D from 6D, Prog. Theor. Phys. 104 (2000) 835 [hep-ph/0006231] [INSPIRE].
K. Hanaki, K. Ohashi and Y. Tachikawa, Supersymmetric completion of an R 2 term in five-dimensional supergravity, Prog. Theor. Phys. 117 (2007) 533 [hep-th/0611329] [INSPIRE].
E. Bergshoeff, M. de Roo and B. de Wit, Extended conformal supergravity, Nucl. Phys. B 182 (1981) 173 [INSPIRE].
G. Lopes Cardoso, B. de Wit, J. Käppeli and T. Mohaupt, Stationary BPS solutions in N = 2 supergravity with R 2 interactions, JHEP 12(2000) 019 [hep-th/0009234] [INSPIRE].
B. de Wit, S. Katmadas and M. van Zalk, New supersymmetric higher-derivative couplings: full N = 2 superspace does not count!, JHEP 01 (2011) 007 [arXiv:1010.2150] [INSPIRE].
A. Castro, J.L. Davis, P. Kraus and F. Larsen, 5D black holes and strings with higher derivatives, JHEP 06 (2007) 007 [hep-th/0703087] [INSPIRE].
A. Castro, J.L. Davis, P. Kraus and F. Larsen, Precision entropy of spinning black holes, JHEP 09 (2007) 003 [arXiv:0705.1847] [INSPIRE].
A. Castro, J.L. Davis, P. Kraus and F. Larsen, String theory effects on five-dimensional black hole physics, Int. J. Mod. Phys. A 23 (2008) 613 [arXiv:0801.1863] [INSPIRE].
B. de Wit and S. Katmadas, Near-horizon analysis of D = 5 BPS black holes and rings, JHEP 02 (2010) 056 [arXiv:0910.4907] [INSPIRE].
B. de Wit, B. Kleijn and S. Vandoren, Superconformal hypermultiplets, Nucl. Phys. B 568 (2000) 475 [hep-th/9909228] [INSPIRE].
B. de Wit, P. Lauwers and A. Van Proeyen, Lagrangians of N = 2 supergravity-matter systems, Nucl. Phys. B 255 (1985) 569 [INSPIRE].
B. de Wit and A. Van Proeyen, Potentials and symmetries of general gauged N = 2 supergravity: Yang-Mills models, Nucl. Phys. B 245 (1984) 89 [INSPIRE].
S. Ferrara and B. Zumino, Structure of conformal supergravity, Nucl. Phys. B 134 (1978) 301 [INSPIRE].
S. Ferrara and P. Van Nieuwenhuizen, Structure of supergravity, Phys. Lett. B 78 (1978) 573 [INSPIRE]
P. Townsend and P. van Nieuwenhuizen, Anomalies, topological invariants and the Gauss-Bonnet theorem in supergravity, Phys. Rev. D 19 (1979) 3592 [INSPIRE].
R. Grimm, J. Wess and B. Zumino, A complete solution of the Bianchi identities in superspace, Nucl. Phys. B 152 (1979) 255 [INSPIRE].
A. Sen, Logarithmic corrections to N = 2 black hole entropy: an infrared window into the microstates, arXiv:1108.3842 [INSPIRE].
J.P. Gauntlett and J.B. Gutowski, General concentric black rings, Phys. Rev. D 71 (2005) 045002 [hep-th/0408122] [INSPIRE].
I. Bena and P. Kraus, Microscopic description of black rings in AdS/CFT, JHEP 12 (2004) 070 [hep-th/0408186] [INSPIRE].
M. Cyrier, M. Guica, D. Mateos and A. Strominger, Microscopic entropy of the black ring, Phys. Rev. Lett. 94 (2005) 191601 [hep-th/0411187] [INSPIRE].
I. Bena, P. Kraus and N.P. Warner, Black rings in Taub-NUT, Phys. Rev. D 72 (2005) 084019 [hep-th/0504142] [INSPIRE].
I. Bena and P. Kraus, R 2 corrections to black ring entropy, hep-th/0506015 [INSPIRE].
K. Hanaki, K. Ohashi and Y. Tachikawa, Comments on charges and near-horizon data of black rings, JHEP 12 (2007) 057 [arXiv:0704.1819] [INSPIRE].
M. Henneaux and C. Teitelboim, Quantization of topological mass in the presence of a magnetic pole, Phys. Rev. Lett. 56 (1986) 689 [INSPIRE].
X. Bekaert, Issues in electric magnetic duality, hep-th/0209169 [INSPIRE].
X. Bekaert and A. Gomberoff, Quantization of the Chern-Simons coupling constant, JHEP 01 (2003) 054 [hep-th/0212099] [INSPIRE].
B. de Wit, J. van Holten and A. Van Proeyen, Structure of N = 2 supergravity, Nucl. Phys. B 184 (1981) 77 [Erratum ibid. B 222 (1983) 516] [INSPIRE].
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ArXiv ePrint: 1112.5371
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Banerjee, N., de Wit, B. & Katmadas, S. The off-shell 4D/5D connection. J. High Energ. Phys. 2012, 61 (2012). https://doi.org/10.1007/JHEP03(2012)061
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DOI: https://doi.org/10.1007/JHEP03(2012)061