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Journal Article

Lifshitz as a deformation of Anti-de Sitter


Korovin,  Yegor
KdV Institute for Mathematics;
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Korovin, Y., Skenderis, K., & Taylor, M. (2013). Lifshitz as a deformation of Anti-de Sitter. Journal of high energy physics: JHEP, 2013(08): 026. doi:10.1007/JHEP08(2013)026.

Cite as: http://hdl.handle.net/11858/00-001M-0000-0029-7014-6
We consider holography for Lifshitz spacetimes with dynamical exponent z=1+epsilon^2, where epsilon is small. We show that the holographically dual field theory is a specific deformation of the relativistic CFT, corresponding to the z=1 theory. Treating epsilon as a small expansion parameter we set up the holographic dictionary for Einstein-Proca models up to order epsilon^2 in three and four bulk dimensions. We explain how renormalization turns the relativistic conformal invariance into non-relativistic Lifshitz invariance with dynamical exponent z=1+epsilon^2. We compute the two-point function of the conserved spin two current for the dual two-dimensional field theory and verify that it is Lifshitz invariant. Using only QFT arguments, we show that a particular class of deformations of CFTs generically leads to Lifshitz scaling invariance and we construct examples of such deformations.