paper

Conformal Lifshitz Gravity from Holography

arXiv:1112.5660 · doi:10.1007/JHEP05(2012)010

Abstract

We show that holographic renormalization of relativistic gravity in asymptotically Lifshitz spacetimes naturally reproduces the structure of gravity with anisotropic scaling: The holographic counterterms induced near anisotropic infinity take the form of the action for gravity at a Lifshitz point, with the appropriate value of the dynamical critical exponent . In the particular case of 3+1 bulk dimensions and asymptotic scaling near infinity, we find a logarithmic counterterm, related to anisotropic Weyl anomaly of the dual CFT, and show that this counterterm reproduces precisely the action of conformal gravity at a Lifshitz point in 2+1 dimensions, which enjoys anisotropic local Weyl invariance and satisfies the detailed balance condition. We explain how the detailed balance is a consequence of relations among holographic counterterms, and point out that a similar relation holds in the relativistic case of holography in . Upon analytic continuation, analogous to the relativistic case studied recently by Maldacena, the action of conformal gravity at the Lifshitz point features in the ground-state wavefunction of a gravitational system with an interesting type of spatial anisotropy.

41 pages; v2: typos corrected, references added

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