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Schrödinger-like Dilaton Gravity

We investigate possibilities for a Schrödinger-like gravity with the dynamical critical exponent z=2, where the action only contains the first-order time derivative. The Horava gravity always admits such a relevant deformation because the full (d+1) dimensional diffeomorphism of the Einstein gravity...

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Bibliographic Details
Main Author: Nakayama, Yu
Format: Article
Language:English
Published: Інститут математики НАН України 2011
Series:Symmetry, Integrability and Geometry: Methods and Applications
Online Access:http://dspace.nbuv.gov.ua/handle/123456789/146794
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Summary:We investigate possibilities for a Schrödinger-like gravity with the dynamical critical exponent z=2, where the action only contains the first-order time derivative. The Horava gravity always admits such a relevant deformation because the full (d+1) dimensional diffeomorphism of the Einstein gravity is replaced by the foliation preserving diffeomorphism. The dynamics is locally trivial or topological in the pure gravity case, but we can construct a dynamical field theory with a z=2 dispersion relation by introducing a dilaton degree of freedom. Our model provides a classical starting point for the possible quantum dilaton gravity which may be applied to a membrane quantization.