Bulk Local States and Crosscaps in Holographic CFT

TL;DR

This paper explores the relationship between bulk local states and crosscaps in holographic CFTs, revealing incompatibilities between causality and bootstrap constraints, and suggesting a different organization of states in three dimensions.

Contribution

It demonstrates that bulk state constraints from causality and bootstrap are incompatible in weak gravity, and provides evidence that 3D bulk states are not organized by Virasoro symmetry.

Findings

Causality and bootstrap constraints are incompatible in weak gravity.

Bulk local states in 3D are not organized by Virasoro symmetry.

Evidence suggests alternative organization of bulk states in 3D.

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.