Causal Structures and Nonlocality in Double Holography

TL;DR

This paper investigates the causal structures in double holography, revealing a compatibility between bulk and BCFT causality, while identifying a necessary long-range nonlocal effect in the intermediate theory to maintain consistency.

Contribution

It demonstrates the compatibility of bulk and BCFT causal structures and uncovers a long-range nonlocal effect required in the intermediate theory for consistency.

Findings

Bulk and BCFT causality are compatible due to a generalized Gao-Wald theorem.

The intermediate theory must include superluminal, nonlocal effects at long range.

Confirmed nonlocality through geometrical analysis and microscopic field commutators.

Abstract

Double holography plays a crucial role in recent studies of Hawking radiation and information paradox by relating an intermediate picture, in which a dynamical gravity living on an end-of-the-world brane is coupled to a non-gravitational heat bath, to a much better-understood BCFT picture as well as a bulk picture. In this paper, causal structures in generic double holographic setups are studied. We find that the causal structure in the bulk picture is compatible with causality in the BCFT picture, thanks to a generalization of the Gao-Wald theorem. On the other hand, consistency with the bulk causal structure requires the effective theory in the intermediate picture to contain a special type of superluminal and nonlocal effect which is significant at long range or IR. These are confirmed by both geometrical analysis and commutators of microscopic fields. Subregion correspondences in double holography are discussed with the knowledge of this nonlocality. Possible fundamental origins of this nonlocality and its difference with other types of nonlocality will also be discussed.