Abstract
We analyze some properties of the four dimensional supergravity theories which originate from five dimensions upon reduction. They generalize to N > 2 extended supersymmetries the d-geometries with cubic prepotentials, familiar from N = 2 special Kähler geometry. We emphasize the role of a suitable parametrization of the scalar fields and the corresponding triangular symplectic basis. We also consider applications to the first order flow equations for non-BPS extremal black holes.
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References
M. Günaydin, G. Sierra and P. Townsend, The Geometry of N = 2 Maxwell-Einstein Supergravity and Jordan Algebras, Nucl. Phys. B 242 (1984) 244 [INSPIRE].
B. de Wit and A. Van Proeyen, Special geometry, cubic polynomials and homogeneous quaternionic spaces, Commun. Math. Phys. 149 (1992) 307 [hep-th/9112027] [INSPIRE].
B. de Wit, F. Vanderseypen and A. Van Proeyen, Symmetry structure of special geometries, Nucl. Phys. B 400 (1993) 463 [hep-th/9210068] [INSPIRE].
S. Cecotti, S. Ferrara and L. Girardello, Geometry of Type II Superstrings and the Moduli of Superconformal Field Theories, Int. J. Mod. Phys. A 4 (1989) 2475 [INSPIRE].
E. Cremmer, C. Kounnas, A. Van Proeyen, J. Derendinger, S. Ferrara and L. Girardello, Vector Multiplets Coupled to N = 2 Supergravity: SuperHiggs Effect, Flat Potentials and Geometric Structure, Nucl. Phys. B 250 (1985) 385 [INSPIRE].
E. Cremmer and A. Van Proeyen, Classification of Kähler manifolds in N = 2 vector multiplet supergravity couplings, Class. Quant. Grav. 2 (1985) 445 [INSPIRE].
A. Ceresole, S. Ferrara and A. Marrani, 4d/5d Correspondence for the Black Hole Potential and its Critical Points, Class. Quant. Grav. 24 (2007) 5651 [arXiv:0707.0964] [INSPIRE].
A. Ceresole, S. Ferrara, A. Gnecchi and A. Marrani, More on N = 8 Attractors, Phys. Rev. D 80 (2009) 045020 [arXiv:0904.4506] [INSPIRE].
A. Ceresole, S. Ferrara and A. Gnecchi, 5d/4d U-dualities and N = 8 black holes, Phys. Rev. D 80 (2009) 125033 [arXiv:0908.1069] [INSPIRE].
M.K. Gaillard and B. Zumino, Duality Rotations for Interacting Fields, Nucl. Phys. B 193 (1981) 221 [INSPIRE].
C. Hull and P. Townsend, Unity of superstring dualities, Nucl. Phys. B 438 (1995) 109 [hep-th/9410167] [INSPIRE].
S. Ferrara and M. Günaydin, Orbits of exceptional groups, duality and BPS states in string theory, Int. J. Mod. Phys. A 13 (1998) 2075 [hep-th/9708025] [INSPIRE].
M. Duff, J.T. Liu and J. Rahmfeld, Four-dimensional string-string-string triality, Nucl. Phys. B 459 (1996) 125 [hep-th/9508094] [INSPIRE].
K. Behrndt, R. Kallosh, J. Rahmfeld, M. Shmakova and W.K. Wong, STU black holes and string triality, Phys. Rev. D 54 (1996) 6293 [hep-th/9608059] [INSPIRE].
S. Ferrara and R. Kallosh, On N = 8 attractors, Phys. Rev. D 73 (2006) 125005 [hep-th/0603247] [INSPIRE].
L. Andrianopoli, R. D’Auria and S. Ferrara, U duality and central charges in various dimensions revisited, Int. J. Mod. Phys. A 13 (1998) 431 [hep-th/9612105] [INSPIRE].
A. Strominger, Special geometry, Commun. Math. Phys. 133 (1990) 163 [INSPIRE].
A. Ceresole, R. D’Auria, S. Ferrara and A. Van Proeyen, Duality transformations in supersymmetric Yang-Mills theories coupled to supergravity, Nucl. Phys. B 444 (1995) 92 [hep-th/9502072] [INSPIRE].
A. Ceresole, R. D’Auria, S. Ferrara and A. Van Proeyen, On electromagnetic duality in locally supersymmetric N = 2 Yang-Mills theory, in Proceedings of Physics from Planck scale to electroweak scale, KU Leuven Press, Theoretical Physics Section, (1994), pg. 390-423, [hep-th/9412200] [INSPIRE].
S. Cecotti and C. Vafa, Topological antitopological fusion, Nucl. Phys. B 367 (1991) 359 [INSPIRE].
A. Ceresole, R. D’Auria, S. Ferrara, W. Lerche and J. Louis, Picard-Fuchs equations and special geometry, Int. J. Mod. Phys. A 8 (1993) 79 [hep-th/9204035] [INSPIRE].
A. Ceresole, G. Dall’Agata, S. Ferrara and A. Yeranyan, First order flows for N = 2 extremal black holes and duality invariants, Nucl. Phys. B 824 (2010) 239 [arXiv:0908.1110] [INSPIRE].
A. Ceresole, G. Dall’Agata, S. Ferrara and A. Yeranyan, Universality of the superpotential for D = 4 extremal black holes, Nucl. Phys. B 832 (2010) 358 [arXiv:0910.2697] [INSPIRE].
M. Günaydin, G. Sierra and P. Townsend, Exceptional Supergravity Theories and the MAGIC Square, Phys. Lett. B 133 (1983) 72 [INSPIRE].
P. Jordan, J. von Neumann and E.P. Wigner, On an Algebraic generalization of the quantum mechanical formalism, Annals Math. 35 (1934) 29.
G. Bossard, Y. Michel and B. Pioline, Extremal black holes, nilpotent orbits and the true fake superpotential, JHEP 01 (2010) 038 [arXiv:0908.1742] [INSPIRE].
A. Ceresole and G. Dall’Agata, Flow Equations for Non-BPS Extremal Black Holes, JHEP 03 (2007) 110 [hep-th/0702088] [INSPIRE].
R. Kallosh, private communication.
B. de Wit and A. Van Proeyen, Broken σ-model isometries in very special geometry, Phys. Lett. B 293 (1992) 94 [hep-th/9207091] [INSPIRE].
L. Andrianopoli, R. D’Auria, S. Ferrara and M. Lledó, Gauging of flat groups in four-dimensional supergravity, JHEP 07 (2002) 010 [hep-th/0203206] [INSPIRE].
E. Cremmer and B. Julia, The N = 8 Supergravity Theory. 1. The Lagrangian, Phys. Lett. B 80 (1978) 48 [INSPIRE].
E. Cremmer and B. Julia, The SO(8) Supergravity, Nucl. Phys. B 159 (1979) 141 [INSPIRE].
S. Ferrara and R. Kallosh, Supersymmetry and attractors, Phys. Rev. D 54 (1996) 1514 [hep-th/9602136] [INSPIRE].
E. Cremmer, B. Julia, H. Lü and C. Pope, Dualization of dualities. 2. Twisted selfduality of doubled fields and superdualities, Nucl. Phys. B 535 (1998) 242 [hep-th/9806106] [INSPIRE].
C. Bunster and M. Henneaux, The Action for Twisted Self-Duality, Phys. Rev. D 83 (2011) 125015 [arXiv:1103.3621] [INSPIRE].
L. Andrianopoli, R. D’Auria, S. Ferrara and M. Trigiante, Extremal black holes in supergravity, Lect. Notes Phys. 737 (2008) 661 [hep-th/0611345] [INSPIRE].
P. Aschieri, S. Ferrara and B. Zumino, Duality Rotations in Nonlinear Electrodynamics and in Extended Supergravity, Riv. Nuovo Cim. 31 (2008) 625 [arXiv:0807.4039] [INSPIRE].
S. Ferrara, R. Kallosh and A. Van Proeyen, Conjecture on Hidden Superconformal Symmetry of N = 4 Supergravity, Phys. Rev. D 87 (2013) 025004 [arXiv:1209.0418] [INSPIRE].
E. Cremmer, J. Scherk and S. Ferrara, SU(4) Invariant Supergravity Theory, Phys. Lett. B 74 (1978) 61 [INSPIRE].
B.L. Cerchiai, S. Ferrara, A. Marrani and B. Zumino, Duality, Entropy and ADM Mass in Supergravity, Phys. Rev. D 79 (2009) 125010 [arXiv:0902.3973] [INSPIRE].
L. Andrianopoli, R. D’Auria, E. Orazi and M. Trigiante, First order description of black holes in moduli space, JHEP 11 (2007) 032 [arXiv:0706.0712] [INSPIRE].
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ArXiv ePrint: 1210.5983v2
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Ceresole, A., Ferrara, S., Gnecchi, A. et al. d-geometries revisited. J. High Energ. Phys. 2013, 59 (2013). https://doi.org/10.1007/JHEP02(2013)059
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DOI: https://doi.org/10.1007/JHEP02(2013)059