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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

13 Citations (Scopus)

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 languageEnglish (US)
Title of host publicationThe Attractor Mechanism - Proceedings of the INFN-Laboratori Nazionali di Frascati School 2007
EditorsStefano Bellucci
PublisherSpringer Science and Business Media, LLC
Pages31-84
Number of pages54
ISBN (Print)9783642107351
DOIs
StatePublished - Jan 1 2010
Event3rd School on Attractor Mechanisms, SAM 2007 - Frascati, Italy
Duration: Jun 18 2007Jun 22 2007

Publication series

NameSpringer Proceedings in Physics
Volume134
ISSN (Print)0930-8989
ISSN (Electronic)1867-4941

Other

Other3rd School on Attractor Mechanisms, SAM 2007
CountryItaly
CityFrascati
Period6/18/076/22/07

Fingerprint

lectures
supergravity
harmonics
symmetry
Jordan
equivalence
algebra
scalars
orbits
formulations

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

Cite this

Gunaydin, M. (2010). Lectures on spectrum generating symmetries and u-duality in supergravity, extremal black holes, quantum attractors and harmonic superspace. In S. Bellucci (Ed.), 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
Gunaydin, Murat. / Lectures on spectrum generating symmetries and u-duality in supergravity, extremal black holes, quantum attractors and harmonic superspace. The Attractor Mechanism - Proceedings of the INFN-Laboratori Nazionali di Frascati School 2007. editor / Stefano Bellucci. Springer Science and Business Media, LLC, 2010. pp. 31-84 (Springer Proceedings in Physics).
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Gunaydin, M 2010, Lectures on spectrum generating symmetries and u-duality in supergravity, extremal black holes, quantum attractors and harmonic superspace. in S Bellucci (ed.), 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.

The Attractor Mechanism - Proceedings of the INFN-Laboratori Nazionali di Frascati School 2007. ed. / Stefano Bellucci. Springer Science and Business Media, LLC, 2010. p. 31-84 (Springer Proceedings in Physics; Vol. 134).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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Gunaydin M. Lectures on spectrum generating symmetries and u-duality in supergravity, extremal black holes, quantum attractors and harmonic superspace. In Bellucci S, editor, The Attractor Mechanism - Proceedings of the INFN-Laboratori Nazionali di Frascati School 2007. Springer Science and Business Media, LLC. 2010. p. 31-84. (Springer Proceedings in Physics). https://doi.org/10.1007/978-3-642-10736-8_2