Abstract
We compute dispersion relations of non-hydrodynamic and hydrodynamic modes in a non-relativistic strongly coupled two-dimensional quantum field theory. This is achieved by numerically computing quasinormal modes (QNMs) of a particular analytically known black brane solution to 3+1-dimensional Hǒrava Gravity. Hǒrava Gravity is distinguished from Einstein Gravity by the presence of a scalar field, termed the khronon, defining a preferred time-foliation. Surprisingly, for this black brane solution, the khronon fluctuation numerically decouples from all others, having its own set of purely imaginary eigenfrequencies, for which we provide an analytic expression. All other Hǒrava Gravity QNMs are expressed analytically in terms of QNMs of Einstein Gravity, in units involving the khronon coupling constants and various horizons. Our numerical computation reproduces the analytically known momentum diffusion mode, and extends the analytic expression for the sound modes to a wide range of khronon coupling values. In the eikonal limit (large momentum limit), the analytically known dispersion of QNM frequencies with the momentum is reproduced by our numerics. We provide a parametrization of all QNM frequencies to fourth order in the momentum. We demonstrate perturbative stability in a wide range of coupling constants and momenta.
Highlights
Horava coupling constant to zero, λ = 0
quasinormal modes (QNMs) data is collected in the supplementary material attached to this paper
The theory is comprised of two sectors, the parity even polar sector, and the parity odd axial sector
Summary
We will summarize those aspects of Horava Gravity of relevance to our calculation of QNMs. Our main interest are all the QNMs of fluctuations around a particular analytically known Horava black brane solution found by Janiszewski [11]. The degrees of freedom are represented by GIJ , N I , and N , which are constituents of the ADM decomposition of the spacetime metric, gXY ;4 where we will be using the mostly positive metric convention.. In terms of spacetime coordinates xX = {t, r, x, y} the line element is given by ds2 = gXY dxX dxY = −N 2dt2 + GIJ (dxI + N I dt)(dxJ + N J dt). In (3+1) dimensions the analytically known metric solution [11] satisfies the equations of motion generated by the variation of the following action of Horava Gravity: SHorava =. These allowed regions of parameter space are represented by white surfaces plus the blue line along the β-axis in the (β,λ)-parameter plots figure 1 and figure 2; forbidden regions are colored red
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