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Wormholes without averaging

Saad, Phil, Shenker, Stephen H., Stanford, Douglas, Yao, Shunyu·2024·Journal of High Energy Physics
DOI 10.1007/jhep09(2024)133
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Abstract

A bstract: After averaging over fermion couplings, SYK has a collective field description that sometimes has “wormhole” solutions. We study the fate of these wormholes when the couplings are fixed. Working mainly in a simple model, we find that the wormhole saddles persist, but that new saddles also appear elsewhere in the integration space — “half-wormholes.” The wormhole contributions depend only weakly on the specific choice of couplings, while the half-wormhole contributions are strongly sensitive. The half-wormholes are crucial for factorization of decoupled systems with fixed couplings, but they vanish after averaging, leaving the non-factorizing wormhole behind.

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Crossref · 10.1007/jhep09(2024)133

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Figures

Image 1
CC-BY · From the PDF
Figure 1 We plot the complex σ plane. Outside the blue scalloped curve, the trivial saddle point dominates, and Φ( σ ) is self-averaging. The black dots are the locations of the 'wormhole' saddle points. They are in the self-averaging region: wormholes persist.
Figure 1 We plot the complex σ plane. Outside the blue scalloped curve, the trivial saddle point dominates, and Φ( σ ) is self-averaging. The black dots are the locations of the 'wormhole' saddle points. They are in the self-averaging region: wormholes persist.CC-BY · From the PDF
Image 3
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Image 4
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Figure 2 We plot six different samples of the integrand for z 2 , namely Φ( σ )Ψ( σ ) . Solid lines with different colors denote different samples. The black dashed line is the exact RMS value of the integrand using (2.31), and the red dashed line is the exact averaged value, using (2.30). Here N = 40 , q = 2 . The wormhole saddle for 〈 z 2 〉 is at a value σ = 1 , which is not within the self-averaging region.
Figure 2 We plot six different samples of the integrand for z 2 , namely Φ( σ )Ψ( σ ) . Solid lines with different colors denote different samples. The black dashed line is the exact RMS value of the integrand using (2.31), and the red dashed line is the exact averaged value, using (2.30). Here N = 40 , q = 2 . The wormhole saddle for 〈 z 2 〉 is at a value σ = 1 , which is not within the self-averaging region.CC-BY · From the PDF
Image 6
CC-BY · From the PDF
Figure 3 The solid blue curve is the logarithm of the RMS value of the integrand along the ray σ = re i π 4 , namely 1 N log(Φ rms ( e i π 4 r ) 2 ) -3 4 r 4 3 . The dashed red curve is the logarithm of the averaged value of this integrand, namely 1 N log(Φ mean ( e i π 4 r ) 2 ) -3 4 r 4 3 . The wormhole saddle point is at r = 1 , and the half-wormhole is at r = 0 . For the plot we took N = 100 and q = 4 . (We don't know how to make a plot with samples for q > 2 because Φ( σ ) seems to be intractable.)
Figure 3 The solid blue curve is the logarithm of the RMS value of the integrand along the ray σ = re i π 4 , namely 1 N log(Φ rms ( e i π 4 r ) 2 ) -3 4 r 4 3 . The dashed red curve is the logarithm of the averaged value of this integrand, namely 1 N log(Φ mean ( e i π 4 r ) 2 ) -3 4 r 4 3 . The wormhole saddle point is at r = 1 , and the half-wormhole is at r = 0 . For the plot we took N = 100 and q = 4 . (We don't know how to make a plot with samples for q > 2 because Φ( σ ) seems to be intractable.)CC-BY · From the PDF

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Cites

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Research works printed but not linked: 42

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Metadata

Authors
Saad, P., Shenker, S. H., Stanford, D., & Yao, S.
Venue
Journal of High Energy Physics
Publisher
Springer Science and Business Media LLC
Published
2024-09-19
Volume
2024
Issue
9
ISSN
1029-8479
DOI
10.1007/jhep09(2024)133
Cited by
31
References
9
Language
en
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CoChat. (2026). Citation check: Wormholes without averaging. https://app.cochat.ai/papers/10.1007/jhep09(2024)133
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Saad, P., Shenker, S. H., Stanford, D., & Yao, S. (2024). Wormholes without averaging. Journal of High Energy Physics. https://doi.org/10.1007/jhep09(2024)133