On the Causality Paradox and the Karch-Randall Braneworld as an EFT

TL;DR

This paper investigates causality in holographic models with cutoff surfaces, demonstrating that apparent superluminal signals are UV effects and proposing modified causal regions to preserve causality in the Karch-Randall braneworld.

Contribution

It clarifies how causality violations are effective theory artifacts and introduces three candidate causal regions to address superluminal signalling in holographic models.

Findings

Causality violations are not visible above the cutoff length scale.

Different candidate regions exclude superluminally affected parts of the domain.

In two dimensions, all candidate regions agree; in higher dimensions, they differ.

Abstract

Holography on cutoff surfaces can appear to be in tension with causality. For example, as argued by Omiya and Wei [arxiv:2107.01219], double holography seemingly allows for superluminal signalling. In this paper we argue that the brane description of double holography should be treated as an effective theory and demonstrate that causality violations due to faster-than-light communication are not visible above the associated cutoff length scale. This suggests that end-of-the-world brane models are consistent with causality and that the apparent superluminal signalling is a UV effect. Moreover, we argue that short distance non-localities generically give rise to apparent faster-than-light propagation of signals in Anti-de Sitter space. Nonetheless, superluminal signalling indicates that the causal structure on holographic cutoff surfaces needs to be modified. We propose and study three different candidate regions that might replace the domain of dependence in the brane EFT of the Karch-Randall model. These regions are defined by unitarity on the brane, through bulk entanglement wedges and through the nice slice criterion, respectively. In all dimensions, these candidate regions exclude those parts of the domain of dependence which are affected by superluminal signalling. While all three definitions agree in two dimensions, they are different in higher dimensions.