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Communications in Mathematical Physics

, Volume 302, Issue 3, pp 755–788 | Cite as

Sugawara-Type Constraints in Hyperbolic Coset Models

  • Thibault Damour
  • Axel Kleinschmidt
  • Hermann Nicolai
Article

Abstract

In the conjectured correspondence between supergravity and geodesic models on infinite-dimensional hyperbolic coset spaces, and E 10/K(E 10) in particular, the constraints play a central role. We present a Sugawara-type construction in terms of the E 10 Noether charges that extends these constraints infinitely into the hyperbolic algebra, in contrast to the truncated expressions obtained in Damour et al. (Class. Quant. Grav. 24:6097, 2007) that involved only finitely many generators. Our extended constraints are associated to an infinite set of roots which are all imaginary, and in fact fill the closed past light-cone of the Lorentzian root lattice. The construction makes crucial use of the E 10 Weyl group and of the fact that the E 10 model contains both D = 11 supergravity and D = 10 IIB supergravity. Our extended constraints appear to unite in a remarkable manner the different canonical constraints of these two theories. This construction may also shed new light on the issue of ‘open constraint algebras’ in traditional canonical approaches to gravity.

Keywords

Weyl Group Dynkin Diagram Level Decomposition High Weight Vector Maximal Supergravity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Thibault Damour
    • 1
  • Axel Kleinschmidt
    • 2
  • Hermann Nicolai
    • 3
  1. 1.Institut des Hautes Etudes ScientifiquesBures-sur-YvetteFrance
  2. 2.Physique Théorique et MathématiqueUniversité Libre de Bruxelles & International Solvay InstitutesBruxellesBelgium
  3. 3.Max-Planck-Insitut für Gravitationsphysik, Albert-Einstein-InstitutPotsdamGermany

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