Comments on Holography with Broken Lorentz Invariance

TL;DR

This paper analyzes solutions of Einstein equations with broken Lorentz invariance, clarifies their relationships, and confirms the duality correspondence with boundary scalar field theories, advancing understanding of holography in non-Lorentz-invariant backgrounds.

Contribution

It shows that recent solutions are part of earlier solutions in extra dimensional theories, establishing parameter relations and confirming duality for known solutions.

Findings

Correct reproduction of scalar two-point correlation functions at critical parameters

Clarification of the relationship between different Lorentz-violating solutions

Completion of the holographic dictionary for these solutions

Abstract

Recently a family of solutions of Einstein equations in backgrounds with broken Lorentz invariance was found ArXiv:0712.1136. We show that the gravitational solution recently obtained by Kachru, Liu and Mulligan in ArXiv:0808.1725 is a part of the former solution which was derived earlier in the framework of extra dimensional theories. We show how the energy-momentum and Einstein tensors are related and establish a correspondence between parameters which govern Lorentz invariance violation. Then we demonstrate that scaling behavior of two point correlation functions of local operators in scalar field theory is reproduced correctly for two cases with critical values of scaling parameters. Therefore, we complete the dictionary of "tree-level" duality for all known solutions of the bulk theory. In the end we speculate on relations between RG flow of a boundary theory and asymptotic behavior of gravitational solutions in the bulk.