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From Path Integrals to Tensor Networks for AdS/CFT

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arxiv 1609.04645 v2 pith:GENB35E7 submitted 2016-09-15 hep-th quant-ph

Masamichi Miyaji , Tadashi Takayanagi , Kento Watanabe This is my paper · ORCID
classification hep-thquant-ph
keywords ads3path-integralquantumscaleslicestatetensortime
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In this paper, we discuss tensor network descriptions of AdS/CFT from two different viewpoints. First, we start with an Euclidean path-integral computation of ground state wave functions with a UV cut off. We consider its efficient optimization by making its UV cut off position dependent and define a quantum state at each length scale. We conjecture that this path-integral corresponds to a time slice of AdS. Next, we derive a flow of quantum states by rewriting the action of Killing vectors of AdS3 in terms of the dual 2d CFT. Both approaches support a correspondence between the hyperbolic time slice H2 in AdS3 and a version of continuous MERA (cMERA). We also give a heuristic argument why we can expect a sub-AdS scale bulk locality for holographic CFTs.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Does Boundary Distinguish Complexities?

    hep-th 2019-08 conditional novelty 6.0 of 10

    In BCFT, boundary complexity increments show the same divergent structure for volume, action, and path-integral measures in d>2, but in d=2 the action measure gives a finite constant instead of a logarithmic divergence.

  2. The Baby Universe is Fine and the CFT Knows It: On Holography for Closed Universes

    hep-th 2025-07 conditional novelty 5.0 of 10

    A closed universe in AdS/CFT is not ruled out by recent SWAP-test arguments; the one-dimensional Hilbert space seen from the CFT is external indistinguishability, and CFT data can reconstruct the closed universe's geometry.

  3. Reflections on Virasoro circuit complexity and Berry phase

    hep-th 2019-08 reject novelty 3.0 of 10

    A claimed identification of Virasoro circuit complexity with the Berry connection fails a basic consistency check for pure rotations.

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