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Random statistics of OPE coefficients and Euclidean wormholes

Belin, Alexandre, de Boer, Jan·2021·Classical and Quantum Gravity
DOI 10.1088/1361-6382/ac1082
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Abstract

We propose an ansatz for OPE coefficients in chaotic conformal field theories which generalizes the eigenstate thermalization hypothesis and describes any OPE coefficient involving heavy operators as a random variable with a Gaussian distribution. In two dimensions this ansatz enables us to compute higher moments of the OPE coefficients and analyse two and four-point functions of OPE coefficients, which we relate to genus-2 partition functions and their squares. We compare the results of our ansatz to solutions of Einstein gravity in AdS 3 , including a Euclidean wormhole that connects two genus-2 surfaces. Our ansatz reproduces the non-perturbative correction of the wormhole, giving it a physical interpretation in terms of OPE statistics. We propose that calculations performed within the semi-classical low-energy gravitational theory are only sensitive to the random nature of OPE coefficients, which explains the apparent lack of factorization in products of partition functions.

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Crossref · 10.1088/1361-6382/ac1082

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Figures

Figure 1 A genus-2 surface with three cycles highlighted. One handlebody solution corresponds to a solid filing of the genus-2 surface such that the three red cycles are made contractible in the bulk.
Figure 1 A genus-2 surface with three cycles highlighted. One handlebody solution corresponds to a solid filing of the genus-2 surface such that the three red cycles are made contractible in the bulk.CC-BY · From the PDF
Figure 2 The Euclidean wormhole (26) connecting through the bulk two genus-2 surfaces that were originally disconnected.
Figure 2 The Euclidean wormhole (26) connecting through the bulk two genus-2 surfaces that were originally disconnected.CC-BY · From the PDF
Figure 3 A handlebody where the three blue cycles are made contractible in the bulk. This saddle is equivalent to decomposing the genus two partition function such that the three blue cycles are cut open. This yields a sum over OPE coefficients ∑ i , j , k CiijC jkk , corresponding to a product of torus one-point functions.
Figure 3 A handlebody where the three blue cycles are made contractible in the bulk. This saddle is equivalent to decomposing the genus two partition function such that the three blue cycles are cut open. This yields a sum over OPE coefficients ∑ i , j , k CiijC jkk , corresponding to a product of torus one-point functions.CC-BY · From the PDF

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Citations

Cites

Research works printed but not linked: 28

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Metadata

Authors
Belin, A., & de Boer, J.
Venue
Classical and Quantum Gravity
Publisher
IOP Publishing
Published
2021-07-16
Volume
38
Issue
16
Pages
164001
ISSN
  • 0264-9381
  • 1361-6382
DOI
10.1088/1361-6382/ac1082
Cited by
131
References
6
Licence
Funders
  • European Research Council
  • NWO (680-47-464 / 4114)
  • ERC (ADG 834878)
  • European Unions Seventh Framework Programme (FP7/2007-2013)

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