Gravity duals of Lifshitz-like fixed points

Abstract

We find candidate macroscopic gravity duals for scale-invariant but non-Lorentz invariant fixed points, which do not have particle number as a conserved quantity. We compute two-point correlation functions which exhibit novel behavior relative to their AdS counterparts, and find holographic renormalization group flows to conformal field theories. Our theories are characterized by a dynamical critical exponent z, which governs the anisotropy between spatial and temporal scaling t → λ z t, x → λx; we focus on the case with z = 2. Such theories describe multicritical points in certain magnetic materials and liquid crystals, and have been shown to arise at quantum critical points in toy models of the cuprate superconductors. This work can be considered a small step towards making useful dual descriptions of such critical points.

Lifshitz scale anomalies

“…Lifshitz scaling shows up also in certain solutions to Einstein gravity with matter (e.g. [9]), and in deformations of Anti-de-Sitter [10].…”

Transport properties of spacetime-filling branes

“…To name a few, holographic superconductivity was first constructed using a minimal set of matter fields and gravity [4], and only later string theory embeddings were studied [5][6][7]. The same happened for theories with Lifshitz or Schrödinger scaling, proposed in [8] and [9] respectively and then obtained from string theory in [10][11][12]. A different application of bottom-up models is a phenomenological approach.…”

“…The longitudinal fluctuation of the electric field gives information about the diffusion of charge in the system via a hydrodynamic pole with dispersion relation 28) with D the diffusion constant, as described by Fick's law ∂ t φ = D∂ 2 x φ. 8 The hydrodynamic mode associated to the scalar perturbations of the metric consists of the sound mode, with dispersion relation 29) where the hydrodynamic prediction for c is the speed of sound (2.20), and for the attenuation coefficient is Γ = η E+P . In holographic setups based on Einstein gravity with space isotropy, like the model studied here, the shear viscosity is related to the entropy via the KSS value η s = 1 4π [33,39].…”

Lorentz violation, gravity, dissipation and holography

“…The three previous special solutions violate the Gubser bound conditions in (B.5). The scalar curvature is constant when θ = 0 (pure Lifshitz case, [96]). The figure 1 displays the constraints of the Gubser bound in (B.5) for gapless and gapped geometries.…”