Bulk Local States and Crosscaps in Holographic CFT

TL;DR

The work analyzes how bulk locality in AdS is encoded in the dual CFT via crosscap Ishibashi states, showing that microscopic bulk causality and crosscap bootstrap constraints are generally incompatible in the weakly coupled regime. It develops a detailed comparison between bulk local states and crosscap states, revealing that crosscaps naturally contain infinite towers of multi-trace Ishibashi components, while bulk local states are dominated by single-trace content in the appropriate limit. In 2d, Virasoro symmetry can enhance the structure of crosscaps, but the authors provide evidence that bulk local states do not admit a universal Virasoro organization, as demonstrated by explicit Ising-model analyses. Overall, the paper argues that bootstrap data alone do not uniquely characterize bulk locality, and Virasoro symmetry does not universally solve the causality constraints in AdS/CFT.

Abstract

In a weakly coupled gravity theory in the anti-de Sitter space, local states in the bulk are linear superpositions of Ishibashi states for a crosscap in the dual conformal field theory. The superposition structure can be constrained either by the microscopic causality in the bulk gravity or the bootstrap condition in the boundary conformal field theory. We show, contrary to some expectation, that these two conditions are not compatible to each other in the weak gravity regime. We also present an evidence to show that bulk local states in three dimensions are not organized by the Virasoro symmetry.