Non-geometric States in a Holographic Conformal Field Theory

Abstract

In the AdS${}_3$/CFT${}_2$ correspondence, we find some conformal field theory (CFT) states that have no bulk description by the Bañados geometry. We elaborate the constraints for a CFT state to be geometric, i.e., having a dual Bañados metric, by comparing the order of central charge of the entanglement/Rényi entropy obtained respectively from the holographic method and the replica trick in CFT. We find that the geometric CFT states fulfill Bohr's correspondence principle by reducing the quantum KdV hierarchy to its classical counterpart. We call the CFT states that satisfy the geometric constraints geometric states, and otherwise non-geometric states. We give examples of both the geometric and non-geometric states, with the latter case including the superposition states and descendant states.

19 pages, v2 match the published version

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Cited by in corpus (7)

• Entanglement spectrum of geometric states
• Entanglement of purification and disentanglement in CFTs
• Entanglement of Purification and Projective Measurement in CFT
• Rényi entropy at large energy density in 2D CFT
• The area operator and fixed area states in conformal field theories
• Perturbative distinguishability of black hole microstates from AdS/CFT correspondence
• Spectral Projections for Density Matrices in Quantum Field Theories