From path integrals to tensor networks for the AdS/CFT correspondence

DOI HANDLE Web Site Web Site 8 Citations 42 References Open Access
  • Miyaji, Masamichi
    Center for Gravitational Physics, Yukawa Institute for Theoretical Physics (YITP), Kyoto University
  • Takayanagi, Tadashi
    Center for Gravitational Physics, Yukawa Institute for Theoretical Physics (YITP), Kyoto University･Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU), University of Tokyo
  • Watanabe, Kento
    Center for Gravitational Physics, Yukawa Institute for Theoretical Physics (YITP), Kyoto University

Bibliographic Information

Other Title
  • From path integrals to tensor networks for the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>AdS</mml:mi><mml:mo>/</mml:mo><mml:mi>CFT</mml:mi></mml:mrow></mml:math> correspondence

Abstract

In this paper, we discuss tensor network descriptions of AdS/CFT from two different viewpoints. First, we start with a Euclidean path-integral computation of ground state wave functions with a UV cutoff. We consider its efficient optimization by making its UV cutoff position dependent and define a quantum state at each length scale. We conjecture that this path integral corresponds to a time slice of anti–de Sitter (AdS) spacetime. Next, we derive a flow of quantum states by rewriting the action of Killing vectors of AdS₃ in terms of the dual two-dimensional conformal field theory (CFT). Both approaches support a correspondence between the hyperbolic time slice H₂ in AdS₃ and a version of continuous multiscale entanglement renormalization ansatz. We also give a heuristic argument about why we can expect a sub-AdS scale bulk locality for holographic CFTs.

Journal

  • Physical Review D

    Physical Review D 95 (6), 066004-, 2017-03-15

    American Physical Society (APS)

Citations (8)*help

See more

References(42)*help

See more

Related Projects

See more

Details 詳細情報について

Report a problem

Back to top