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Caputa P, Kundu N, Miyaji M, et al. Anti-de Sitter Space from Optimization of Path Integrals in Conformal Field Theories. Phys Rev Lett. 2017;119(7):071602doi: 10.1103/PhysRevLett.119.071602.
Caputa, P., Kundu, N., Miyaji, M., Takayanagi, T., & Watanabe, K. (2017). Anti-de Sitter Space from Optimization of Path Integrals in Conformal Field Theories. Physical review letters, 119(7), 071602. https://doi.org/10.1103/PhysRevLett.119.071602
Caputa, Pawel, et al. "Anti-de Sitter Space from Optimization of Path Integrals in Conformal Field Theories." Physical review letters vol. 119,7 (2017): 071602. doi: https://doi.org/10.1103/PhysRevLett.119.071602
Caputa P, Kundu N, Miyaji M, Takayanagi T, Watanabe K. Anti-de Sitter Space from Optimization of Path Integrals in Conformal Field Theories. Phys Rev Lett. 2017 Aug 18;119(7):071602. doi: 10.1103/PhysRevLett.119.071602. Epub 2017 Aug 18. PMID: 28949666.
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Phys Rev Lett. 2017 Aug 18;119(7):071602. doi: 10.1103/PhysRevLett.119.071602. Epub 2017 Aug 18.

Anti-de Sitter Space from Optimization of Path Integrals in Conformal Field Theories.

Physical review letters

Pawel Caputa, Nilay Kundu, Masamichi Miyaji, Tadashi Takayanagi, Kento Watanabe

Affiliations

  1. Center for Gravitational Physics, Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa Oiwakecho, Sakyo-ku, Kyoto 606-8502, Japan.
  2. Kavli Institute for the Physics and Mathematics of the Universe, University of Tokyo, Kashiwa, Chiba 277-8582, Japan.

PMID: 28949666 DOI: 10.1103/PhysRevLett.119.071602

Abstract

We introduce a new optimization procedure for Euclidean path integrals, which compute wave functionals in conformal field theories (CFTs). We optimize the background metric in the space on which the path integration is performed. Equivalently, this is interpreted as a position-dependent UV cutoff. For two-dimensional CFT vacua, we find the optimized metric is given by that of a hyperbolic space, and we interpret this as a continuous limit of the conjectured relation between tensor networks and Anti-de Sitter (AdS)/conformal field theory (CFT) correspondence. We confirm our procedure for excited states, the thermofield double state, the Sachdev-Ye-Kitaev model, and discuss its extension to higher-dimensional CFTs. We also show that when applied to reduced density matrices, it reproduces entanglement wedges and holographic entanglement entropy. We suggest that our optimization prescription is analogous to the estimation of computational complexity.

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