On a lightlike limit of entanglement

TL;DR

This paper investigates the behavior of holographic entanglement entropy in lightlike limits of excited states within nonrelativistic holography, revealing milder divergences and potential ultralocality in ground states.

Contribution

It introduces a novel analysis of lightlike limits of entanglement entropy in holographic theories, connecting geometric deformations to entanglement properties in excited and ground states.

Findings

Null limit entanglement divergence is milder than the area law.

Entanglement vanishes in ground states, indicating ultralocality.

Excited states show nonvanishing correlators in free lightfront theories.

Abstract

We study certain classes of $g_{++}$ deformations of theories arising in gauge/string realizations of nonrelativistic holography, some of which pertain to $z=2$ Lifshitz theories while others (pertaining to hyperscaling violation) comprise certain classes of excited states. Building on previous work, we consider holographic entanglement entropy for spacelike strip subsystems in a highly boosted (lightlike) limit, where the strip is stretched along the null $x^+$-plane. The leading divergence in entanglement in this null limit for these excited states is milder than the usual area law for spacelike subsystems in ground states. For ground states, the entanglement vanishes, perhaps consistent with ultralocality. We discuss this briefly from a field theory perspective. We also present some simple free lightfront field theory examples in excited states where correlators are nonvanishing.