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On the causality paradox and the Karch-Randall braneworld as an EFT

Neuenfeld, Dominik, Srivastava, Manu·2023·Journal of High Energy Physics
DOI 10.1007/jhep10(2023)164
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Abstract

A bstract: Holography on cutoff surfaces can appear to be in tension with causality. For example, as argued by Omiya and Wei [1], double holography seemingly allows for superluminal signalling. In this paper we argue that the brane description of double holography should be treated as an effective theory and demonstrate that causality violations due to faster-than-light communication are not visible above the associated cutoff length scale. This suggests that end-of-the-world brane models are consistent with causality and that the apparent superluminal signalling is a UV effect. Moreover, we argue that short distance non-localities generically give rise to apparent faster-than-light propagation of signals in Anti-de Sitter space. Nonetheless, superluminal signalling indicates that the causal structure on holographic cutoff surfaces needs to be modified. We propose and study three different candidate regions that might replace the domain of dependence in the brane EFT of the Karch-Randall model. These regions are defined by unitarity on the brane, through bulk entanglement wedges and through the nice slice criterion, respectively. In all dimensions, these candidate regions exclude those parts of the domain of dependence which are affected by superluminal signalling. While all three definitions agree in two dimensions, they are different in higher dimensions.

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Figures

Figure 1 The three descriptions in double holography. (a) The boundary description consists of a BCFT on the asymptotic boundary M coupled to a large number of degrees of freedom at its boundary (black square). (b) The bulk description is given by anti-de Sitter space with asymptotic boundary M and cut off by an end-of-the-world brane Q . (c) The brane description consists of a non-gravitational CFT on M which can exchange excitations with an effective CFT on Q coupled to gravity.
Figure 1 The three descriptions in double holography. (a) The boundary description consists of a BCFT on the asymptotic boundary M coupled to a large number of degrees of freedom at its boundary (black square). (b) The bulk description is given by anti-de Sitter space with asymptotic boundary M and cut off by an end-of-the-world brane Q . (c) The brane description consists of a non-gravitational CFT on M which can exchange excitations with an effective CFT on Q coupled to gravity.CC-BY · From the PDF
Figure 2 Covariant computation of cutoff on the brane. The radius r of the smallest sphere on the imagined asymptotic boundary such that the entanglement wedge touches the point p is r = y p cot µ ∗ .
Figure 2 Covariant computation of cutoff on the brane. The radius r of the smallest sphere on the imagined asymptotic boundary such that the entanglement wedge touches the point p is r = y p cot µ ∗ .CC-BY · From the PDF
Figure 3 The configurations of points q, p, p ′ used to show that causality violations by faster-than-light signalling cannot be resolved in the effective theory, since the spatial (a) and temporal (b) resolution is too low.
Figure 3 The configurations of points q, p, p ′ used to show that causality violations by faster-than-light signalling cannot be resolved in the effective theory, since the spatial (a) and temporal (b) resolution is too low.CC-BY · From the PDF
Figure 4 We can send a plane wave to the left or to the right. (a) If we send the light front from the boundary towards the brane, the light front on the brane moves at c eff . (b) If we send it from the brane towards the asymptotic boundary, the light front moves with c .
Figure 4 We can send a plane wave to the left or to the right. (a) If we send the light front from the boundary towards the brane, the light front on the brane moves at c eff . (b) If we send it from the brane towards the asymptotic boundary, the light front moves with c .CC-BY · From the PDF
Figure 5 A simple model for finite size excitations on a AdS Karch-Randall brane. The center of excitations, denoted by the black dot, moves at bulk the speed of light c . The leading edge moves with c eff .
Figure 5 A simple model for finite size excitations on a AdS Karch-Randall brane. The center of excitations, denoted by the black dot, moves at bulk the speed of light c . The leading edge moves with c eff .CC-BY · From the PDF
Figure 6 ∂ + E α ( B ) is the future boundary on the EFT domain of dependence of B .
Figure 6 ∂ + E α ( B ) is the future boundary on the EFT domain of dependence of B .CC-BY · From the PDF
Figure 7 Configurations of subregions for which subadditivity is tested.
Figure 7 Configurations of subregions for which subadditivity is tested.CC-BY · From the PDF
Figure 8 Comparing bounds on C ( B ) with D eff ( B ) and D ( B ) for strip regions on d = 3 dimensional branes ( y 1 = 2000, y 2 = 10000). The AdS length scale L and the bulk/boundary speed of light c have been set to 1. In this figure, as well as in all the following ones, we only plot t > 0 since the plots are symmetric under time-reversal.
Figure 8 Comparing bounds on C ( B ) with D eff ( B ) and D ( B ) for strip regions on d = 3 dimensional branes ( y 1 = 2000, y 2 = 10000). The AdS length scale L and the bulk/boundary speed of light c have been set to 1. In this figure, as well as in all the following ones, we only plot t > 0 since the plots are symmetric under time-reversal.CC-BY · From the PDF
Figure 9 Left: The slope of the SA bound at the end location closer to the defect approaches 1 /c R eff = sin µ ∗ in the limit of large subregions. Right: The slope of the SA bound at the end location away from the defect approaches -1 /c L eff = -1 in the limit of large subregions. These plots correspond to the case of a d = 3 dimensional brane located at µ ∗ = 1. The AdS length scale L and the bulk/boundary speed of light c have been set to 1.
Figure 9 Left: The slope of the SA bound at the end location closer to the defect approaches 1 /c R eff = sin µ ∗ in the limit of large subregions. Right: The slope of the SA bound at the end location away from the defect approaches -1 /c L eff = -1 in the limit of large subregions. These plots correspond to the case of a d = 3 dimensional brane located at µ ∗ = 1. The AdS length scale L and the bulk/boundary speed of light c have been set to 1.CC-BY · From the PDF
Figure 10 Comparing H ( B ), D eff ( B ) and D ( B ) for strip regions on d = 3 dimensional branes ( y 1 = 2000, y 2 = 10000). The AdS length scale L and the bulk/boundary speed of light c have been set to 1.
Figure 10 Comparing H ( B ), D eff ( B ) and D ( B ) for strip regions on d = 3 dimensional branes ( y 1 = 2000, y 2 = 10000). The AdS length scale L and the bulk/boundary speed of light c have been set to 1.CC-BY · From the PDF
Figure 11 Comparing E α ( B ), D eff ( B ) and D ( B ) for strip regions on d = 3 dimensional branes ( y 1 = 2000, y 2 = 10000). The AdS length scale L and the bulk/boundary speed of light c have been set to 1.
Figure 11 Comparing E α ( B ), D eff ( B ) and D ( B ) for strip regions on d = 3 dimensional branes ( y 1 = 2000, y 2 = 10000). The AdS length scale L and the bulk/boundary speed of light c have been set to 1.CC-BY · From the PDF
Figure 12 Comparing H ( B ) and E α ( B ) and bound on C ( B ) for strip regions on d = 2 dimensional branes ( y 1 = 2000, y 2 = 10000). The constantK curve for α = 1, the SA bound and the intersection of the EW with the brane all coincide exactly. The AdS length scale L and the bulk/boundary speed of light c have been set to 1.
Figure 12 Comparing H ( B ) and E α ( B ) and bound on C ( B ) for strip regions on d = 2 dimensional branes ( y 1 = 2000, y 2 = 10000). The constantK curve for α = 1, the SA bound and the intersection of the EW with the brane all coincide exactly. The AdS length scale L and the bulk/boundary speed of light c have been set to 1.CC-BY · From the PDF
Figure 13 Comparing H ( B ) and E α ( B ) and bound on C ( B ) ( y 1 = 2000, y 2 = 10000) for µ ∗ = 1 . 0 (top panel) and µ ∗ = 1 . 3 (bottom panel). The AdS length scale L and the bulk/boundary speed of light c have been set to 1.
Figure 13 Comparing H ( B ) and E α ( B ) and bound on C ( B ) ( y 1 = 2000, y 2 = 10000) for µ ∗ = 1 . 0 (top panel) and µ ∗ = 1 . 3 (bottom panel). The AdS length scale L and the bulk/boundary speed of light c have been set to 1.CC-BY · From the PDF
Figure 14 Illustrating intersection of the entanglement wedge with the brane
Figure 14 Illustrating intersection of the entanglement wedge with the braneCC-BY · From the PDF
Figure 15 The dotted lines are the boundary of the region in which sub-additivity holds, i.e., the bound on C ( B ). y 1 = 50, y 2 = 200 and the solid lines represent the curves traced by eq. (B.4) for different µ ∗ 's.
Figure 15 The dotted lines are the boundary of the region in which sub-additivity holds, i.e., the bound on C ( B ). y 1 = 50, y 2 = 200 and the solid lines represent the curves traced by eq. (B.4) for different µ ∗ 's.CC-BY · From the PDF

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Metadata

Authors
Neuenfeld, D., & Srivastava, M.
Affiliations
  • Julius-Maximilians-Universität Würzburg
  • Massachusetts Institute of Technology
ORCID
Venue
Journal of High Energy Physics
Publisher
Springer Science and Business Media LLC
Published
2023-10-26
Volume
2023
Issue
10
ISSN
1029-8479
DOI
10.1007/jhep10(2023)164
Cited by
13
References
8
Language
en
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