Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2010-07-08
Phys.Rev.D82:084002,2010; Erratum-ibid.D82:109905,2010
Physics
High Energy Physics
High Energy Physics - Theory
24 pages, 4 figures, references added, published in PRD, conclusions modified
Scientific paper
10.1103/PhysRevD.82.084002 10.11
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.
Hoyos Carlos
Koroteev Peter
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