On the Null Energy Condition and Causality in Lifshitz Holography
arXiv:1007.1428 · doi:10.1103/PhysRevD.82.084002 10.1103/PhysRevD.82.109905
Abstract
We use a WKB approximation to establish a relation between the wavefront velocity in a strongly coupled theory and the local speed of light in a holographic dual, with our main focus put on systems with Lifshitz scaling with dynamical exponent z. We then use Einstein equations to relate the behavior of the local speed of light in the bulk with the null energy condition (NEC) for bulk matter, and we show that it is violated for Lifshitz backgrounds with z<1. We study signal propagation in the gravity dual and show that violations of the NEC are incompatible with causality in the strongly coupled theory, ruling out as holographic models Lifshitz backgrounds with z<1. We argue that causality violations in z<1 theories will show up in correlators as superluminal modes and confirm this for a particular example with z=1/2. Finally, as an application, we use z<1 solutions to uncover regions of the parameter space of curvature squared corrections to gravity where the NEC can be violated.
24 pages, 4 figures, references added, published in PRD, conclusions modified
References in corpus (16)
- Minkowski-space correlators in AdS/CFT correspondence: recipe and applications
- Toward an AdS/cold atoms correspondence: a geometric realization of the Schroedinger symmetry
- Lectures on Holographic Superfluidity and Superconductivity
- Conformal collider physics: Energy and charge correlations
- Viscosity Bound and Causality Violation
- Seeing a c-theorem with holography
- Non-relativistic holography
- Higher Derivative Gravity, Causality and Positivity of Energy in a UV complete QFT
- Black holes in asymptotically Lifshitz spacetime
- On String Theory Duals of Lifshitz-like Fixed Points
- Light quark energy loss in strongly-coupled N = 4 supersymmetric Yang-Mills plasma
- Jets in strongly-coupled N = 4 super Yang-Mills theory
- 1/N Effects in Non-Relativistic Gauge-Gravity Duality
- Energy Flux Positivity and Unitarity in CFTs
- AdS black holes as reflecting cavities
- Spectra of Field Fluctuations in Braneworld Models with Broken Bulk Lorentz Invariance