Logarithmic two-Point Correlation Functions from a z = 2 Lifshitz Model

Abstract

The Einstein-Proca action is known to have asymptotically locally Lifshitz spacetimes as classical solutions. For dynamical exponent z=2, two-point correlation functions for fluctuations around such a geometry are derived analytically. It is found that the retarded correlators are stable in the sense that all quasinormal modes are situated in the lower half-plane of complex frequencies. Correlators in the longitudinal channel exhibit features that are reminiscent of a structure usually obtained in field theories that are logarithmic, i.e. contain an indecomposable highest weight representation. This suggests the model at hand as a candidate for a gravity dual of a logarithmic field theory with anisotropic scaling symmetry.