Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 7 (2011), 014, 12 pages      arXiv:1001.3436      https://doi.org/10.3842/SIGMA.2011.014

Schrödinger-like Dilaton Gravity

Yu Nakayama a, b
a) Berkeley Center for Theoretical Physics, University of California, Berkeley, CA 94720, USA
b) Institute for the Physics and Mathematics of the Universe, University of Tokyo, Kashiwa, Chiba 277-8582, Japan

Received September 16, 2010, in final form February 02, 2011; Published online February 08, 2011

Abstract
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.

Key words: non-relativistic gravity; membrane quantization.

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