### Abstract

We review the underlying algebraic structures of supergravity theories with symmetric scalar manifolds in five and four dimensions, orbits of their extremal black hole solutions and the spectrum generating extensions of their U-duality groups. For 5D, N = 2 Maxwell–Einstein supergravity theories (MESGT) defined by Euclidean Jordan algebras, J, the spectrum generating symmetry groups are the conformal groups Conf(J) of J which are isomorphic to their U-duality groups in four dimensions. Similarly, the spectrum generating symmetry groups of 4D, N = 2 MESGTs are the quasiconformal groups QConf(J) associated with J that are isomorphic to their U-duality groups in three dimensions. We then review the work on spectrum generating symmetries of spherically symmetric stationary 4D BPS black holes, based on the equivalence of their attractor equations and the equations for geodesic motion of a fiducial particle on the target spaces of corresponding 3D supergravity theories obtained by timelike reduction. We also discuss the connection between harmonic superspace formulation of 4D, N = 2 sigma models coupled to supergravity and the minimal unitary representations of their isometry groups obtained by quantizing their quasiconformal realizations. We discuss the relevance of this connection to spectrum generating symmetries and conclude with a brief summary of more recent results.

Original language | English (US) |
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Title of host publication | The Attractor Mechanism - Proceedings of the INFN-Laboratori Nazionali di Frascati School 2007 |

Editors | Stefano Bellucci |

Publisher | Springer Science and Business Media, LLC |

Pages | 31-84 |

Number of pages | 54 |

ISBN (Print) | 9783642107351 |

DOIs | |

State | Published - Jan 1 2010 |

Event | 3rd School on Attractor Mechanisms, SAM 2007 - Frascati, Italy Duration: Jun 18 2007 → Jun 22 2007 |

### Publication series

Name | Springer Proceedings in Physics |
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Volume | 134 |

ISSN (Print) | 0930-8989 |

ISSN (Electronic) | 1867-4941 |

### Other

Other | 3rd School on Attractor Mechanisms, SAM 2007 |
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Country | Italy |

City | Frascati |

Period | 6/18/07 → 6/22/07 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)

### Cite this

*The Attractor Mechanism - Proceedings of the INFN-Laboratori Nazionali di Frascati School 2007*(pp. 31-84). (Springer Proceedings in Physics; Vol. 134). Springer Science and Business Media, LLC. https://doi.org/10.1007/978-3-642-10736-8_2

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*The Attractor Mechanism - Proceedings of the INFN-Laboratori Nazionali di Frascati School 2007.*Springer Proceedings in Physics, vol. 134, Springer Science and Business Media, LLC, pp. 31-84, 3rd School on Attractor Mechanisms, SAM 2007, Frascati, Italy, 6/18/07. https://doi.org/10.1007/978-3-642-10736-8_2

**Lectures on spectrum generating symmetries and u-duality in supergravity, extremal black holes, quantum attractors and harmonic superspace.** / Gunaydin, Murat.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Lectures on spectrum generating symmetries and u-duality in supergravity, extremal black holes, quantum attractors and harmonic superspace

AU - Gunaydin, Murat

PY - 2010/1/1

Y1 - 2010/1/1

N2 - We review the underlying algebraic structures of supergravity theories with symmetric scalar manifolds in five and four dimensions, orbits of their extremal black hole solutions and the spectrum generating extensions of their U-duality groups. For 5D, N = 2 Maxwell–Einstein supergravity theories (MESGT) defined by Euclidean Jordan algebras, J, the spectrum generating symmetry groups are the conformal groups Conf(J) of J which are isomorphic to their U-duality groups in four dimensions. Similarly, the spectrum generating symmetry groups of 4D, N = 2 MESGTs are the quasiconformal groups QConf(J) associated with J that are isomorphic to their U-duality groups in three dimensions. We then review the work on spectrum generating symmetries of spherically symmetric stationary 4D BPS black holes, based on the equivalence of their attractor equations and the equations for geodesic motion of a fiducial particle on the target spaces of corresponding 3D supergravity theories obtained by timelike reduction. We also discuss the connection between harmonic superspace formulation of 4D, N = 2 sigma models coupled to supergravity and the minimal unitary representations of their isometry groups obtained by quantizing their quasiconformal realizations. We discuss the relevance of this connection to spectrum generating symmetries and conclude with a brief summary of more recent results.

AB - We review the underlying algebraic structures of supergravity theories with symmetric scalar manifolds in five and four dimensions, orbits of their extremal black hole solutions and the spectrum generating extensions of their U-duality groups. For 5D, N = 2 Maxwell–Einstein supergravity theories (MESGT) defined by Euclidean Jordan algebras, J, the spectrum generating symmetry groups are the conformal groups Conf(J) of J which are isomorphic to their U-duality groups in four dimensions. Similarly, the spectrum generating symmetry groups of 4D, N = 2 MESGTs are the quasiconformal groups QConf(J) associated with J that are isomorphic to their U-duality groups in three dimensions. We then review the work on spectrum generating symmetries of spherically symmetric stationary 4D BPS black holes, based on the equivalence of their attractor equations and the equations for geodesic motion of a fiducial particle on the target spaces of corresponding 3D supergravity theories obtained by timelike reduction. We also discuss the connection between harmonic superspace formulation of 4D, N = 2 sigma models coupled to supergravity and the minimal unitary representations of their isometry groups obtained by quantizing their quasiconformal realizations. We discuss the relevance of this connection to spectrum generating symmetries and conclude with a brief summary of more recent results.

UR - http://www.scopus.com/inward/record.url?scp=84975712884&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84975712884&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-10736-8_2

DO - 10.1007/978-3-642-10736-8_2

M3 - Conference contribution

AN - SCOPUS:84975712884

SN - 9783642107351

T3 - Springer Proceedings in Physics

SP - 31

EP - 84

BT - The Attractor Mechanism - Proceedings of the INFN-Laboratori Nazionali di Frascati School 2007

A2 - Bellucci, Stefano

PB - Springer Science and Business Media, LLC

ER -