Gravity Duals of Lifshitz-like Fixed Points

Gravity Duals of Lifshitz-like Fixed Points

August, 2008 | Shamit Kachru, Xiao Liu, and Michael Mulligan
This paper presents gravity duals for scale-invariant but non-Lorentz invariant fixed points that lack particle number conservation. These duals exhibit novel two-point correlation functions and holographic renormalization group flows to conformal field theories. The theories are characterized by a dynamical critical exponent z, governing the anisotropy between spatial and temporal scaling (t → λ^z t, x → λ x), with a focus on z = 2. Such theories describe multicritical points in magnetic materials and liquid crystals, and arise at quantum critical points in cuprate superconductor models. The authors construct 4D gravity solutions with a negative cosmological constant and p-form gauge fields that support metrics geometrizing the symmetries of Lifshitz-like fixed points. They compute two-point correlation functions for scalar operators, finding that these contain more information than just scaling dimensions. The results show that the correlation functions exhibit non-trivial behavior, including spatially localized terms and power-law decay at large spatial separations. The paper also explores holographic RG flows between z = 2 Lifshitz fixed points and z = 1 conformal field theories, finding solutions that represent such flows. The authors conclude that their work represents a step towards useful dual descriptions of critical points in strongly coupled systems.This paper presents gravity duals for scale-invariant but non-Lorentz invariant fixed points that lack particle number conservation. These duals exhibit novel two-point correlation functions and holographic renormalization group flows to conformal field theories. The theories are characterized by a dynamical critical exponent z, governing the anisotropy between spatial and temporal scaling (t → λ^z t, x → λ x), with a focus on z = 2. Such theories describe multicritical points in magnetic materials and liquid crystals, and arise at quantum critical points in cuprate superconductor models. The authors construct 4D gravity solutions with a negative cosmological constant and p-form gauge fields that support metrics geometrizing the symmetries of Lifshitz-like fixed points. They compute two-point correlation functions for scalar operators, finding that these contain more information than just scaling dimensions. The results show that the correlation functions exhibit non-trivial behavior, including spatially localized terms and power-law decay at large spatial separations. The paper also explores holographic RG flows between z = 2 Lifshitz fixed points and z = 1 conformal field theories, finding solutions that represent such flows. The authors conclude that their work represents a step towards useful dual descriptions of critical points in strongly coupled systems.
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