# Nongeometric states in a holographic conformal field theory

Guo, Wu-zhong (Physics Division, National Center for Theoretical Sciences, National Tsing Hua University, No. 101, Sec. II, Kuang Fu Road, Hsinchu 30013, Taiwan) ; Lin, Feng-Li (Department of Physics, National Taiwan Normal University, No. 88, Sec. IV, Ting-Chou Road, Taipei 11677, Taiwan) ; Zhang, Jiaju (Dipartimento di Fisica G. Occhialini, Università degli Studi di Milano-Bicocca, Piazza della Scienza 3, 20126 Milano, Italy) (INFN, Sezione di Milano-Bicocca, Piazza della Scienza 3, 20126 Milano, Italy)

07 May 2019

Abstract: In the ${\mathrm{AdS}}_{3}/{\mathrm{CFT}}_{2}$ 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 Korteweg-de Vries hierarchy to its classical counterpart. We call the CFT states that satisfy the geometric constraints geometric states, and otherwise, we call them nongeometric states. We give examples of both the geometric and nongeometric states, with the latter case including the superposition states and descendant states.

Published in: Physical Review D 99 (2019)