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Sugawara-type Constraints in Hyperbolic Coset Models

MPS-Authors
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Kleinschmidt,  Axel
Quantum Gravity and Unified Theories, AEI Golm, MPI for Gravitational Physics, Max Planck Society;

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Nicolai,  Hermann
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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0912.3491v1.pdf
(Preprint), 471KB

439687fulltext.pdf
(Any fulltext), 503KB

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Citation

Damour, T., Kleinschmidt, A., & Nicolai, H. (2011). Sugawara-type Constraints in Hyperbolic Coset Models. Communications in Mathematical Physics, 302, 755-788. doi:10.1007/s00220-011-1188-y.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-6146-B
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.