Abstract
We construct operators in holographic two-dimensional conformal field theory, which act locally in the code subspace as arbitrary bulk spacelike vector fields. Key to the construction is an interplay between parallel transport in the bulk spacetime and in kinematic space. We outline challenges, which arise when the same construction is extended to timelike vector fields. We also sketch several applications, including boundary formulations of the bulk Riemann tensor, dreibein, and spin connection, as well as an application to holographic complexity.
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Acknowledgments
We have benefited from conversations with Vijay Balasubramanian, Johanna Erdmenger, Thomas Faulkner, Michał Heller, Ling-Yan (Janet) Hung, Daniel Kabat, Samuel Leutheusser, Gilad Lifschytz, Wei Song, Huajia Wang, Yixu Wang, and Anna-Lena Weigel. BCz thanks the organizers of workshop ‘Quantum Information and String Theory 2019’ held at Yukawa Institute for Theoretical Physics, Kyoto University, where this work was initiated; the organizers of workshop ‘Reconstructing the Gravitational Hologram with Quantum Information’ (2022) held at the Galileo Galilei Institute in Florence, where this work was partly carried out; and the University of Amsterdam for hospitality. Both BCs have been supported by the Dushi Zhuanxiang Fellowship. JdB is supported by the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013), ERC Grant agreement ADG 834878. LL is supported by the Simons Foundation via the It from Qubit Collaboration.
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Chen, B., Czech, B., de Boer, J. et al. Boundary and bulk notions of transport in the AdS3/CFT2 correspondence. J. High Energ. Phys. 2023, 102 (2023). https://doi.org/10.1007/JHEP05(2023)102
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DOI: https://doi.org/10.1007/JHEP05(2023)102