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Author(s): (1) Gopal Yadav, Department of Physics, Indian Institute of Technology & Chennai Mathematical Institute. Table of Links Abstract & Introduction Brief Review of Wedge Holography Emerging Multiverse from Wedge Holography Application to Information Paradox Application to Grandfather Paradox Conclusion Acknowledgements and References Acknowledgements The author is supported by a Senior Research Fellowship (SRF) from the Council of Scientific and Industrial Research (CSIR), Govt. of India. It is my pleasure to thank Aalok Misra, who motivated me to work on the entanglement stuff, and for his blessings. We would also like to thank Juan Maldacena, Andreas Karch, Kostas Skenderis and Tadashi Takayanagi for very helpful discussions and comments. This research was also supported in part by the International Centre for Theoretical Sciences (ICTS) for the program “Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography” (code:ICTS/numstrings-2022/8). Various conferences/workshops; e.g., Mysteries of Universe-I (Institute Lecture Series) and Indian Strings Meeting 2021 at Indian Institute of Technology Roorkee, Roorkee, India; Applications of Quantum Information in QFT and Cosmology at the University of Lethbridge, Canada; Kavli Asian Winter School (KAWS) on Strings, Particles and Cosmology (Online) at International Centre for Theoretical Sciences (ICTS) Bangalore, India (code:ICTS/kaws2022/1); Reconstructing the Gravitational Hologram with Quantum Information at Galileo Galilei Institute for Theoretical Physics, Florence, Italy; Quantum Information in QFT and AdS/CFT-III at Indian Institute of Technology Hyderabad, India; helped me to learn about the information paradox and related stuff. I am very thankful to the speakers and organizers of these conferences because I learned about the subject from these conferences. References [1] S.W. Hawking, Particle Creation by Black Holes, Commun. Math. Phys. 43, 199 (1975) Erratum: [Commun. Math. Phys. 46, 206 (1976)]. [2] D.N. Page, Information in Black Hole Radiation, Phys.Rev.Lett. 71 (1993) 3743-3746 [arXiv:hep-th/9306083 [hep-th]]. [3] J. M. Maldacena, The Large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38, 1113-1133 (1999) [arXiv:hep-th/9711200]. [4] Y. Ling et al, Reflected entropy in double holography, JHEP 02 (2022) 037 [arXiv:2109.09243]. [5] C. Krishnan, Critical Islands, JHEP 01 (2021) 179 [arXiv:2007.06551[hep-th]]. [6] E. Caceres, A. Kundu, Ayan K. Patra and S. Shashi, Page Curves and Bath Deformations [arXiv:2107.00022 [hep-th]]. [7] E. Caceres, A. Kundu, Ayan K. Patra and S. Shashi, Warped information and entanglement islands in AdS/WCFT, JHEP 07 (2021) 004 [arXiv:2012.05425 [hep-th]]. [8] A. Bhattacharya, A. Bhattacharyya, P. Nandy and A.K. Patra, Islands and complexity of eternal black hole and radiation subsystems for a doubly holographic model, JHEP 05 (2021) 135 [arXiv:2103.15852[hep-th]]. [9] A. Bhattacharya, A. Bhattacharyya, P. Nandy and A.K. Patra, Bath deformations, islands and holographic complexity, Phys. Rev. D 105 (2022) 066019 [arXiv:2112.06967[hep-th]]. [10] Q.L. Hu, D. Li, R.X. Miao and Y.Q. Zeng, AdS/BCFT and Island for curvature-squared gravity, [arXiv:2202.03304[hep-th]]. [11] Y. Ling, Y. Liu and Z. Y. Xian, Island in Charged Black Holes, JHEP 03 (2021) 251 [arXiv:2010.00037[hep-th]]. [12] H. Omiya and Z. Wei, Causal Structures and Nonlocality in Double Holography [arXiv:2107.01219[hep-th]]. [13] H. Geng, A. Karch, C.P. Pardavila, S. Raju and L. Randall, Entanglement Phase Structure of a Holographic BCFT in a Black Hole Background, [arXiv:2112.09132[hep-th]]. [14] M. Afrasiar, J.K. Basak, A. Chandra and G. Sengupta, Islands for Entanglement Negativity in Communicating Black Holes [arXiv:2205.07903[hep-th]]. [15] D. Basu, H. Parihar, V. Raj and G. Sengupta, Defect extremal surfaces for entanglement negativity [arXiv:2205.07905[hep-th]]. [16] Y. Liu, Z.Y. Xian, C. Peng and Y. Ling, Black holes Entangled by Radiation, [arXiv:2205.14596[hep-th]]. [17] Z. Li and R.Q. Yang, Upper bounds of holographic entanglement entropy growth rate for thermofield double states, [arXiv:2205.15154[hep-th]]. [18] F. Deng, Y.S. An and Y. Zhou, JT Gravity from Partial Reduction and Defect Extremal Surface, [arXiv:2206.09609[hep-th]]. [19] C.F. Uhlemann, Islands and Page curves in 4d from Type IIB, JHEP 08 (2021) 104 [arXiv:2105.00008[hep-th]]. [20] S. Demulder, A. Gnecchi, I. Lavdas and D. Lust, Island and Light Gravitons in type IIB String Theory, [arXiv:2204.03669[hep-th]]. [21] A. Karch, H. Sun and C.F. Uhlemann, Double holography in string theory, [arXiv:2206.11292[hep-th]]. [22] H. Geng, Y. Nomura and H. Y. Sun, Information paradox and its resolution in de Sitter holography, Phys.Rev.D 103 (2021) 12, 126004 [arXiv:2103.07477[hep-th]]. [23] G. Yadav and A. Misra, (“Swiss-Cheese”) Entanglement Entropy when Page-ing M Theory Dual of Thermal QCD above Tc at Intermediate Coupling, [arXiv:2207.04048[hep-th]]. [24] H. Geng, L. Randall and E. Swanson, BCFT in a Black Hole Background: An Analytical Holographic Model, JHEP 12 (2022) 056 [arXiv:2209.02074[hep-th]]. [25] M. Afrasiar, J. K. Basak, A. Chandra and G. Sengupta, Reflected Entropy for Communicating Black Holes I: Karch-Randall Braneworlds, [arXiv:2211.13246[hep-th]]. [26] A. Karch and L. Randall, Locally localized gravity, JHEP 05 (2001) 008 [hep-th/0011156]. [27] A. Karch and L. Randall, Open and closed string interpretation of SUSY CFT’s on branes with boundaries, JHEP 06 (2001) 063 [hep-th/0105132]. [28] A. Almheiri, R. Mahajan, J. Maldacena and Y. Zhao, The Page curve of Hawking radiation from semiclassical geometry, JHEP 03 (2020) 143 [1908.10996]. [29] S. Ryu, T. Takayanagi, Holographic Derivation of Entanglement Entropy from AdS/CFT, Phys. Rev. Lett. 96, 181602 (2006) [arXiv:hep-th/0603001]. [30] T. Hartman and J. Maldacena, Time Evolution of Entanglement Entropy from Black Hole Interiors, JHEP 05 (2013) 014 [arXiv:1303.1080[hep-th]]. [31] O. Aharony, O. DeWolfe, D.Z. Freedman and A. Karch, Defect conformal field theory and locally localized gravity, JHEP 07 (2003) 030 [hep-th/0303249]. [32] H. Geng and A. Karch, Massive islands, JHEP 09 (2020) 121 [arXiv:2006.02438[hep-th]]. [33] H. Geng, A. Karch, C. P. Pardavila, S. Raju and L. Randall, Information Transfer with a Gravitating Bath, SciPost Phys. 10 (2021) 5, 103 [arXiv:2012.04671[hep-th]]. [34] H. Geng, A. Karch, C. P. Pardavila, S. Raju and L. Randall, Inconsistency of islands in theories with long-range gravity, JHEP 01 (2022) 182 [arXiv:2107.03390[hep-th]]. [35] R. X. Miao, Massless Entanglement Island in Wedge Holography, [arXiv:2212.07645[hep-th]]. [36] K. Ghosh and C. Krishnan, Dirichlet baths and the not-so-fine-grained Page curve, JHEP 08 (2021) 119 [arXiv:2103.17253[hep-th]]. [37] G. R. Dvali, G. Gabadadze and M. Porrati, 4D gravity on a brane in 5D Minkowski space, Phys. Lett. B 485 (2000) 208 [hep-th/0005016]. [38] C. Krishnan, V. Patil and J. Pereira, Page Curve and the Information Paradox in Flat Space, [arXiv:2005.02993[hep-th]]. [39] A. Almheiri, T. Hartman, J. Maldacena, E. Shaghoulian and A. Tajdini, The entropy of Hawking radiation, Rev. Mod. Phys. 93, no.3, 035002 (2021) [arXiv:2006.06872 [hep-th]]. [40] C. Krishnan and V. Mohan, Interpreting the Bulk Page Curve: A Vestige of Locality on Holographic Screens, [arXiv:2112.13783[hep-th]]. [41] I. Akal, Y. Kusuki, T. Takayanagi and Z. Wei, Codimension two holography for wedges, Phys. Rev. D 102, 126007 (2020) [arXiv:2007.06800[hep-th]]. [42] R. X. Miao, An exact construction of codimension two holography, JHEP 01 (2021) 150 [arXiv:2009.06263[hep-th]]. [43] S. Choudhury, S. Panda, Entangled de Sitter from Stringy Axionic Bell pair I: An analysis using Bunch Davies vacuum, Eur.Phys.J. C78 (2018) no.1, 52 [arXiv:1708.02265[hep-th]]. [44] S. Choudhury, S. Panda, Quantum entanglement in de Sitter space from Stringy Axion: An analysis using α vacua, Nucl. Physic. B 943 (2019) 114606 [arXiv:1712.08299[hep-th]]. [45] S. Choudhury et al, Circuit Complexity From Cosmological Islands, Symmetry 13 (2021) no. 7, 1301 [arXiv:2012.10234[hep-th]]. [46] S. Choudhury, Entanglement negativity in de Sitter biverse from Stringy Axionic Bell pair: An analysis using Bunch-Davies vacuum, arXiv:2301.05203[hep-th]. [47] P. J. Hu and R. X. Miao, Effective action, spectrum and first law of wedge holography, JHEP 03 (2022)145 [arXiv:2201.02014]. [48] H. Geng, A. Karch, C. P. Pardavila, S. Raju, L. Randall, M. Riojas, and S. Shashi, Jackiw-Teitelboim Gravity from the Karch-Randall Braneworld, Phys.Rev.Lett. 129 (2022) 23, 231601 [arXiv:2206.04695]. [49] H. Geng, Aspects of AdS2 Quantum Gravity and the Karch-Randall Braneworld, JHEP 09
(2022) 024 [arXiv:2206.11277[hep-th]]. [50] N. Ogawa, T. Takayanagi, T. Tsuda and T. Waki, Wedge Holography in Flat Space and Celestial Holography, [arXiv:2207.06735]. [51] N. Engelhardt and A.C. Wall, Quantum Extremal Surfaces: Holographic Entanglement Entropy beyond the Classical Regime, JHEP 01 (2015) 073 [1408.3203]. [52] N. Ogawa, T. Takayanagi, T. Tsuda and T. Waki, Wedge Holography in Flat Space and Celestial Holography, Phys. Rev. D 107, 026001 [arXiv:2207.06735[hep-th]]. [53] A. Strominger, The dS/CFT correspondence, JHEP 10 (2001) 034 [hep-th/0106113]. [54] J.M. Maldacena, Non-Gaussian features of primordial fluctuations in single field inflationary models, JHEP 05 (2003) 013 [astro-ph/0210603]. [55] A. Karch and L. Randall, Geometries with mismatched branes, J. High Energ. Phys. 2020, 166 (2020) [arXiv:2006.10061[hep-th]]. [56] J. M. Penín, K. Skenderis and B. Withers, Massive holographic QFTs in de Sitter, SciPost Phys. 12, 182 (2022) [arXiv:2112.14639[hep-th]]. [57] K. Hashimoto, N. Iizuka, and Y. Matsuo, Islands in Schwarzschild black holes, J. High Energ. Phys. 2020, 85 (2020) [arXiv:2004.05863[hep-th]]. [58] G. Yadav and N. Joshi, Cosmological and black hole islands in multi-event horizon spacetimes, Phys. Rev. D 107, 026009 (2023) [arXiv:2210.00331[hep-th]]. [59] S. Chapman, D. A. Galante, E. D. Kramer, Holographic Complexity and de Sitter Space, J. High Energ. Phys. 2022, 198 (2022) [arXiv:2110.05522[hep-th]]. [60] G. W. Gibbons and S. W. Hawking, Cosmological event horizons, thermodynamics, and particle creation, Phys. Rev. D 15, 2738. [61] O. Y. Kupervasser, Grandfather Paradox in Non-Quantum and Quantum Gravitation Theories, http://dx.doi.org/10.4236/ns.2014.611079. [62] J. H. Baek and K. S. Choi, Islands in Proliferating de Sitter Spaces, [arXiv:2212.14753[hepth]]. [63] J. Maldacena and A. Milekhin, Humanly traversable wormholes, Phys. Rev. D 103, 066007 (2021) [arXiv:2008.06618[hep-th]]. This paper is under CC 4.0 license. available on arxiv

Multiverse in Karch-Randall Braneworld: Acknowledgements and References

Well, something like that any way. This is a common UI pattern that is a bit difficult to achieve in Elm. Something like render props from the React world or if you have escaped from the angular world. transclusion The idea is that you would like to create a generic component to provide perhaps some wrapper UI and a little bit of state management and then re-use that component but inject your own view (render prop) into it. Good examples of when you might reach for this technique would be a modal or a tab strip. In these cases you don’t want to rewrite the markup and logic that are generic each time. A modal has a header and a footer and you need to track whether it is open or closed etc, but mostly what you care about when you it is the content for your particular use case. use So what’s the problem? It’s in the types. Let’s try to do it and we will see why it doesn’t immediately work. For the sake of simplicity let’s say that my generic component will basically just be a div and that I would like to be able to render my custom container component but inject custom UI into it. My div will have a header that changes colour when you click it (that’s the state that it tracks internally that I want to abstract away). Let’s try it Our ColourClicker component will have the usual Elm lifecycle since it needs to track this little bit of internal state and it might look something like this initially: type alias Model ={ colour : String } type Msg= ToggleColour init : Modelinit ={ colour = "blue" } update : Msg -> Model -> Modelupdate msg model =case msg ofToggleColour ->toggleColour model toggleColour : Model -> ModeltoggleColour model =case model.colour of"blue" ->{ model | colour = "red" }_ ->{ model | colour = "blue" } view : Model -> List (Html Msg) -> Html Msgview model content =div[ class "colour-clicker" ][ h1[ onClick ToggleColour, style "background" model.colour][ text "This is the magical header" ], div []content] Hopefully this doesn’t need too much explanation. The view function simply allows us to inject content from the consuming code. The code that uses this component might look a bit like this: import ColourClicker as C type alias Model ={ colourClicker : C.Model } init : ( Model, Cmd Msg )init =( { colourClicker = C.init }, Cmd.none ) type Msg= ColourClickerMsg C.Msg update : Msg -> Model -> ( Model, Cmd Msg )update msg model =case msg ofColourClickerMsg subMsg ->letsubModel =C.update subMsg model.colourClickerin( { model | colourClicker = subModel }, Cmd.none ) view : Model -> Html Msgview model =div [ class "demo" ][ h1 [] [ text "Demo of render props technique for Elm" ], Html.map ColourClickerMsg <|C.view model.colourClicker[ div [][ text "This is the content of the colour clicker provided by the parent" ]]] Then end result looks like this and works fine: New feature request Now suppose that I want the content that I inject to contain a button and I want to handle the clicking of that button in my parent component. Like this: type Msg= ColourClickerMsg C.Msg| ButtonClicked update : Msg -> Model -> ( Model, Cmd Msg )update msg model =case msg of... ButtonClicked ->  
        let  
            \_ =  
                Debug.log "Button Clicked!" ()  
        in  
        ( model, Cmd.none ) view : Model -> Html Msgview model =div [ class "demo" ][ h1 [] [ text "Demo of render props technique for Elm" ], Html.map ColourClickerMsg <|C.view model.colourClicker[ div [][ text "Now we need to add a button", button [ onClick ButtonClicked ] [ text "Click me!" ]]]] This is a reasonable thing to want to do. We don’t want the ColourClicker component itself to handle this button click because the logic belongs in the calling component. The ColourClicker should only be responsible for its own state (which is the colour of its header). But we have a problem. Our ColourClicker’s view function expects its content to be of type but we are now trying to pass in so the types do not line up and the compiler (rightly) complains. Html ColourClicker.Msg Html Parent.Msg So what can we do? Let’s follow the types. Firstly, we must make the ColourClicker’s view function accept content with a polymorphic type like this: view : Model -> List (Html parent) -> Html Msg In this signature “parent” is a type parameter to indicate that we do not know what type this Html will have. This gets rid of the previous compiler error but replaces it with a new one. The issue now is that our ColourPicker’s view is trying to embed within a block of which is not allowed. So it is clear that we need to somehow map the Html that has been passed in to coerce it to the right type. Html parent Html ColourPicker.Msg To do this we need to create a new Msg type within the ColourClicker to which to map the parent Msg type, create a function to perform the mapping and call that function when we write out the content: type Msg parent= ToggleColour| Parent parent wrap : Html parent -> Html (Msg parent)wrap =Html.map Parent view : Model -> List (Html parent) -> Html (Msg parent)view model content =div[ class "colour-clicker" ][ h1[ onClick ToggleColour, style "background" model.colour][ text "This is the magical header" ], div [](List.map wrap content)] What we have done is to our own Msg type with the polymorphic parent type such that we can create an instance of our Msg type that the parent msg. Note that all of this is transparent to the calling code and introduces no further complexity. This makes the types line up, but isn’t it just a trick? What happens to our update function? It needs to change as follows: parameterise contains update : Msg parent -> Model -> ( Model, Cmd parent )update msg model =case msg ofToggleColour ->( toggleColour model, Cmd.none ) Parent p ->  
        ( model, Task.perform identity (Task.succeed p) ) First we need to change the return type to allow us to return a . This is unusual — ordinarily it would be . We could do that if we needed to, but in this case we don’t. Remember there is nothing magical about the update function, it’s just a function — we can do what we like. In the branch of the case statement that handles the new message type we simply convert that message into a using the Task api and return it to the caller. Cmd parent Cmd Msg as well Parent parent Cmd The final change required then is to the parent’s update function to handle this new return type correctly. This now looks like this: case msg ofColourClickerMsg subMsg ->let( subModel, subCmd ) =C.update subMsg model.colourClickerin( { model | colourClicker = subModel }, subCmd ) The subCmd that comes out of the update function is already the right type to just return directly from the parent’s update function. It will ultimately get fed back into the update function as the ButtonClicked msg. Everything now compiles! We have really nice idiomatic syntax and we are able to naturally handle the button click at the parent level without the ColourClicker component ever knowing anything about it. We can now reuse the ColourClicker component much more effectively. I’d love to hear other approaches to this problem because it took me a while to figure this out and it seems like such a common requirement. The code for this example can be found . Hope this is useful for someone. here

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