Schrödinger-like Dilaton Gravity

Details Schrödinger-like Dilaton Gravity Schrödinger-like Dilaton Gravity

2010-01-20

arxiv.org/abs/1001.3436v3

SIGMA 7 (2011), 014, 12 pages

Physics

High Energy Physics

High Energy Physics - Theory

Scientific paper

10.3842/SIGMA.2011.014

We investigate possibilities for a Schr\"odinger-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.

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