Abstract
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 but non-diagonalizable highest weight representation. This provides further evidence for conjecturing the model at hand as a candidate for a gravity dual of a logarithmic field theory with anisotropic scaling symmetry.
Highlights
Originally derived from a more phenomenological and bottom-up point of view, but recent years have seem many successful ways to realize them as well by a top-down approach via an embedding into a string theory framework, see e.g. [8,9,10,11,12] to just name a few
This paper dealt with an investigation of perturbations around an asymptotically z = 2 Lifshitz fixed point of the Einstein-Proca action
The main focus was on calculating twopoint correlation functions and what information can be gained from this about the dual Lifshitz scaling invariant field theory
Summary
As mentioned in the introduction, the following treatise deals with a bulk action consisting of Einstein gravity coupled minimally to a Proca field,. S = 2κ (R − 2Λ)v − 4κ (dP ∧ ∗dP + c P ∧ ∗P ) The variation of this action leads to the equations of motion, Gμν + Λgμν = TμPν , d ∗ dP = −c ∗ P ,. As has become standard when investigating asymptotically Lifshitz fixed points of this theory, c and Λ can be parameterized as,. Apart from asymptocically AdS spacetimes, (2.2) is solved by the so-called Lifshitz spacetime [7, 13] with dynamical exponent z, where a tetrad and the massive vector field can be parameterized as follows, e0. I.e. for r → 0, approach the structure of (2.5) can be called asymptotically Lifshitz fixed points of (2.2) and were already studied thoroughly in previous work. What follows is mainly a summary of known results, the reader familiar with this work can likely skip this and go ahead to the section
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