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.
M. Miyaji, T. Numasawa, N. Shiba, T. Takayanagi and K. Watanabe, Continuous multiscale entanglement renormalization ansatz as holographic surface-state correspondence, Phys. Rev. Lett. 115 (2015) 171602 [arXiv:1506.01353] [INSPIRE].
N. Ishibashi, The boundary and crosscap states in conformal field theories, Mod. Phys. Lett. A 4 (1989) 251 [INSPIRE].
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
ArXiv ePrint: 1605.00334
About this article
Cite this article
Nakayama, Y., Ooguri, H. Bulk local states and crosscaps in holographic CFT. J. High Energ. Phys. 2016, 85 (2016). https://doi.org/10.1007/JHEP10(2016)085
- AdS-CFT Correspondence
- Conformal Field Theory
- Space-Time Symmetries