On the Null Energy Condition and Causality in Lifshitz Holography

TL;DR

This paper investigates the relationship between the null energy condition and causality in Lifshitz holography, showing NEC violations for z<1 lead to causality issues, thus constraining holographic models with such scaling.

Contribution

It establishes a link between the local speed of light, the null energy condition, and causality in Lifshitz holography, providing constraints on models with z<1.

Findings

NEC is violated for Lifshitz backgrounds with z<1.

Violations of NEC are incompatible with causality in the dual theory.

Superluminal modes indicate causality violations in z<1 theories.

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.