2011/12/31 by Tom Griffin, Petr Horava, Charles M. Melby-Thompson · 1 citation
Mathematics · Physics and Astronomy · #cond-mat.str-el #gr-qc #hep-th #math.DG
paper · pdf · doi:10.1007/jhep05(2012)010
published as JHEP 1205 (2012) 010 · 41 pages; v2: typos corrected, references added
arxiv created 2012/04/03 · arxiv updated 2015/06/03
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 z. In the particular case of 3+1 bulk dimensions and z=2 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 z=2 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 AdS5. Upon analytic continuation, analogous to the relativistic case studied recently by Maldacena, the action of conformal gravity at the z=2 Lifshitz point features in the ground-state wavefunction of a gravitational system with an interesting type of spatial anisotropy.