Causality Criteria for Island Models

Abstract: Island models offer a compelling resolution of the black hole information paradox, but they also raise persistent questions about causal consistency in effective descriptions. In particular, effective theories arising in double holography can exhibit apparent violations of micro-causality, despite the underlying bulk dynamics being local and causal. The aim of this work is to clarify the physical origin of this phenomenon and to identify the structural features that control causal consistency in island models. We argue that the apparent non-causality in double holography is neither intrinsic to island physics nor a consequence of nonlocal operator reconstruction. Rather, it reflects a mismatch between effective spacetime separation and bulk causal accessibility, a feature already implicit in earlier analyses. Nonlocal reconstruction instead encodes quantum error correction within a restricted code subspace and does not introduce independent propagation channels. Motivated by this perspective, we formulate a structural criterion for micro-causality in effective island descriptions. The criterion consists of three conditions: the absence of independent propagation channels beyond those of the bulk theory, a local bulk-supported operator dictionary, and a consistent matching between effective spacelike separation and dynamically accessible bulk causal curves. When these conditions are satisfied, effective micro-causality follows directly from bulk micro-causality. We apply the criterion to brane world realizations of island models, including the defect-extremal-surface construction, and show that they preserve causal consistency, in contrast to double holography. We further demonstrate that the criterion remains robust in time-dependent processes such as island formation and evaporation.