Unitary realizations of U-duality groups as conformal and quasiconformal groups and extremal black holes of supergravity theories

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

22 Citations (Scopus)

Abstract

We review the current status of the construction of unitary representations of U-duality groups of supergravity theories in five, four and three dimensions. We focus mainly on the maximal N = 8 supergravity theories and on the N = 2 Maxwell-Einstein supergravity (MESGT) theories defined by Jordan algebras of degree three in five dimensions and their descendants in four and three dimensions. Entropies of the extremal black hole solutions of these theories in five and four dimensions are given by certain invariants of their U-duality groups. The five dimensional U-duality groups admit extensions to spectrum generating generalized conformal groups which are isomorphic to the U-duality groups of corresponding four dimensional theories. Similarly, the U-duality groups of four dimensional theories admit extensions to spectrum generating quasiconformal groups that are isomorphic to the corresponding U-duality groups in three dimensions. For example, the group E 8(8) can be realized as a quasiconformal group in the 57 dimensional charge-entropy space of BPS black hole solutions of maximal N = 8 supergravity in four dimensions and leaves invariant "lightlike separations" with respect to a quartic norm. Similarly E 7(7) acts as a generalized conformal group in the 27 dimensional charge space of BPS black hole solutions in five dimensional N = 8 supergravity and leaves invariant "lightlike separations" with respect to a cubic norm. For the exceptional N = 2 Maxwell-Einstein supergravity theory the corresponding quasiconformal and conformal groups are E 8(-24) and E 7(-25), respectively. We outline the oscillator construction of the unitary representations of generalized conformal groups that admit positive energy representations, which include the U-duality groups of N = 2 MESGT's in four dimensions. We conclude with a review of the minimal unitary realizations of U-duality groups that are obtained by quantizations of their quasiconformal actions and discuss in detail the minimal unitary realization of E 8(8).

Original languageEnglish (US)
Title of host publicationFUNDAMENTAL INTERACTIONS AND TWISTOR-LIKE METHODS
Subtitle of host publicationXIX Max Born Symposium
Pages268-287
Number of pages20
DOIs
StatePublished - Apr 25 2005
EventFUNDAMENTAL INTERACTIONS AND TWISTOR-LIKE METHODS: XIX Max Born Symposium - Wroclaw, Poland
Duration: Sep 28 2004Oct 1 2004

Publication series

NameAIP Conference Proceedings
Volume767
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Other

OtherFUNDAMENTAL INTERACTIONS AND TWISTOR-LIKE METHODS: XIX Max Born Symposium
CountryPoland
CityWroclaw
Period9/28/0410/1/04

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supergravity
entropy
Jordan
norms
leaves
energy
space charge
algebra
oscillators

All Science Journal Classification (ASJC) codes

  • Ecology, Evolution, Behavior and Systematics
  • Ecology
  • Plant Science
  • Physics and Astronomy(all)
  • Nature and Landscape Conservation

Cite this

Gunaydin, M. (2005). Unitary realizations of U-duality groups as conformal and quasiconformal groups and extremal black holes of supergravity theories. In FUNDAMENTAL INTERACTIONS AND TWISTOR-LIKE METHODS: XIX Max Born Symposium (pp. 268-287). (AIP Conference Proceedings; Vol. 767). https://doi.org/10.1063/1.1923339
Gunaydin, Murat. / Unitary realizations of U-duality groups as conformal and quasiconformal groups and extremal black holes of supergravity theories. FUNDAMENTAL INTERACTIONS AND TWISTOR-LIKE METHODS: XIX Max Born Symposium. 2005. pp. 268-287 (AIP Conference Proceedings).
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Gunaydin, M 2005, Unitary realizations of U-duality groups as conformal and quasiconformal groups and extremal black holes of supergravity theories. in FUNDAMENTAL INTERACTIONS AND TWISTOR-LIKE METHODS: XIX Max Born Symposium. AIP Conference Proceedings, vol. 767, pp. 268-287, FUNDAMENTAL INTERACTIONS AND TWISTOR-LIKE METHODS: XIX Max Born Symposium, Wroclaw, Poland, 9/28/04. https://doi.org/10.1063/1.1923339

Unitary realizations of U-duality groups as conformal and quasiconformal groups and extremal black holes of supergravity theories. / Gunaydin, Murat.

FUNDAMENTAL INTERACTIONS AND TWISTOR-LIKE METHODS: XIX Max Born Symposium. 2005. p. 268-287 (AIP Conference Proceedings; Vol. 767).

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

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Gunaydin M. Unitary realizations of U-duality groups as conformal and quasiconformal groups and extremal black holes of supergravity theories. In FUNDAMENTAL INTERACTIONS AND TWISTOR-LIKE METHODS: XIX Max Born Symposium. 2005. p. 268-287. (AIP Conference Proceedings). https://doi.org/10.1063/1.1923339