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Multiboundary wormholes and OPE statistics

de Boer, Jan, Liška, Diego, Post, Boris·2024·Journal of High Energy Physics
DOI 10.1007/jhep10(2024)207
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Abstract

A bstract: We derive higher moments in the statistical distribution of OPE coefficients in holographic 2D CFTs, and show that such moments correspond to multiboundary Euclidean wormholes in pure 3D gravity. The n th cyclic non-Gaussian contraction of heavy-heavy-light OPE coefficients follows from crossing symmetry of the thermal n -point function. We derive universal expressions for the cubic and quartic moments and demonstrate that their scaling with the microcanonical entropy agrees with a generalization of the Eigenstate Thermalization Hypothesis. Motivated by this result, we conjecture that the full statistical ensemble of OPE data is fixed by three premises: typicality, crossing symmetry and modular invariance. Together, these properties give predictions for non-factorizing observables, such as the generalized spectral form factor. Using the Virasoro TQFT, we match these connected averages to new on-shell wormhole topologies with multiple boundary components. Lastly, we study and clarify examples where the statistics of heavy operators are not universal and depend on the light operator spectrum. We give a gravitational interpretation to these corrections in terms of Wilson loops winding around non-trivial cycles in the bulk.

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Figures

Image 1
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Image 2
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Figure 1 The three basic crossing moves that relate conformal block decompositions in different channels. From left to right, the moves are called fusion, modular S-transform and braiding.
Figure 1 The three basic crossing moves that relate conformal block decompositions in different channels. From left to right, the moves are called fusion, modular S-transform and braiding.CC-BY · From the PDF
Image 4
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Figure 2 The sequence of moves relating the necklace and OPE channel for the torus four-point function. Depicted below each surface is the corresponding trivalent diagram representing the pair-of-pants decomposition.
Figure 2 The sequence of moves relating the necklace and OPE channel for the torus four-point function. Depicted below each surface is the corresponding trivalent diagram representing the pair-of-pants decomposition.CC-BY · From the PDF
Image 6
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Image 7
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Figure 3 Glueing along the inner torus boundaries in blue produces the punctured-torus wormhole.
Figure 3 Glueing along the inner torus boundaries in blue produces the punctured-torus wormhole.CC-BY · From the PDF
Figure 4 Heegaard splitting of the three-boundary wormhole.
Figure 4 Heegaard splitting of the three-boundary wormhole.CC-BY · From the PDF
Figure 5 The Heegaard splitting described in this section leads to a three-boundary torus wormhole, whose conical defect lines meet in a bulk three-point vertex. The bulk has non-trivial topology (not shown in this figure), arising from the glueing of genus-two handlebodies.
Figure 5 The Heegaard splitting described in this section leads to a three-boundary torus wormhole, whose conical defect lines meet in a bulk three-point vertex. The bulk has non-trivial topology (not shown in this figure), arising from the glueing of genus-two handlebodies.CC-BY · From the PDF
Image 11
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Image 12
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Figure 6 Heegaard splitting of the four-boundary wormhole.
Figure 6 Heegaard splitting of the four-boundary wormhole.CC-BY · From the PDF
Image 14
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Figure 7 The 'skyline' channel decomposition of the genus-three partition function (a) can be thought of, diagrammatically, as a three-dimensional tetrahedron (b) with edges labelled by Liouville momenta P i , i = 1 , . . . , 6. The smooth function appearing in the quartic non-Gaussianity (4.4) has the same symmetries as this tetrahedron. The diagram can equivalently be drawn as a crossing partition of an 'exchange' diagram (c) between four operators, modulo phases.
Figure 7 The 'skyline' channel decomposition of the genus-three partition function (a) can be thought of, diagrammatically, as a three-dimensional tetrahedron (b) with edges labelled by Liouville momenta P i , i = 1 , . . . , 6. The smooth function appearing in the quartic non-Gaussianity (4.4) has the same symmetries as this tetrahedron. The diagram can equivalently be drawn as a crossing partition of an 'exchange' diagram (c) between four operators, modulo phases.CC-BY · From the PDF
Figure 8 Heegaard splitting of the non-Gaussian genus-two wormhole.
Figure 8 Heegaard splitting of the non-Gaussian genus-two wormhole.CC-BY · From the PDF
Figure 9 Crossing moves relating the genus-two block in the dumbbell (left) and sunset (right) channels.
Figure 9 Crossing moves relating the genus-two block in the dumbbell (left) and sunset (right) channels.CC-BY · From the PDF
Image 18
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Image 19
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Image 20
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Figure 10 A handlebody with a genus-two boundary whose filling is the outside region of the three-sphere. On the left, the cycle labeled by P 2 is contractible in the bulk. On the right, the same cycle is confined by the Wilson line P χ .
Figure 10 A handlebody with a genus-two boundary whose filling is the outside region of the three-sphere. On the left, the cycle labeled by P 2 is contractible in the bulk. On the right, the same cycle is confined by the Wilson line P χ .CC-BY · From the PDF
Image 22
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Image 23
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Image 24
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Image 25
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Image 26
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Image 27
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Metadata

Authors
de Boer, J., Liška, D., & Post, B.
Venue
Journal of High Energy Physics
Publisher
Springer Science and Business Media LLC
Published
2024-10-29
Volume
2024
Issue
10
ISSN
1029-8479
DOI
10.1007/jhep10(2024)207
Cited by
27
References
5
Language
en
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