Spatial Anisotropy in Nonrelativistic Holography

Abstract

We examine holographic theories where Lifshitz symmetry is broken with spatial anisotropy. In particular, we focus on the conditions imposed by the null energy condition, and demonstrate that it is possible to have unusual anisotropic fixed points where a subset of the spatial dimensions have negative scaling exponents. We also construct interpolating solutions between UV and IR fixed points and show that there is essentially no restriction placed on the endpoints of the flow once anisotropic scaling is allowed. As an example, we demonstrate a flow from AdS to AdS with $c_{IR}>c_{UV}$ that is allowed by the null energy condition since it proceeds through an intermediate Lorentz-violating region. Finally, we examine the holographic Green's function in anisotropic Lifshitz spacetimes.

22 pages, 3 figures, references added

References in corpus (12)

• Minkowski-space correlators in AdS/CFT correspondence: recipe and applications
• Toward an AdS/cold atoms correspondence: a geometric realization of the Schroedinger symmetry
• Gravity duals for non-relativistic CFTs
• Holographic c-theorems in arbitrary dimensions
• Topological Insulators and Nematic Phases from Spontaneous Symmetry Breaking in 2D Fermi Systems with a Quadratic Band Crossing
• Seeing a c-theorem with holography
• Topological Order and Conformal Quantum Critical Points
• Non-relativistic holography
• On String Theory Duals of Lifshitz-like Fixed Points
• Pathologies in Asymptotically Lifshitz Spacetimes
• Conformal field theories in $d=4$ with a helical twist
• Hidden horizons in non-relativistic AdS/CFT

Cited by in corpus (3)

• Black branes in asymptotically Lifshitz spacetime and viscosity/entropy ratios in Horndeski gravity
• Anisotropic Lifshitz holography in Einstein-Proca theory with stable negative mass spectrum
• Kasner-type singularities and solitons with Lifshitz asymptotics