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Aspects of Codimension two Holography in de Sitter Space

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Kanhu Kishore Nanda, Somnath Porey, Masataka Watanabe, Gopal Yadav

High Energy Physics - Theory · Submitted 15 Oct 2026 · 65 references

Pith's verdict: A useful consistency-check paper on dS wedge holography: new Euclidean slicing, scalar correlators, and a DS/dS band, but the pseudo-entropy prescription is imported rather than derived.

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CitationGopal Yadav, Kanhu Kishore Nanda, Masataka Watanabe, Somnath Porey. "Aspects of Codimension two Holography in de Sitter Space." arXiv:2610.22101 (2026). https://pith.science/paper/IYQO7BHY
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The paper

The paper claims

The paper argues that classical gravity inside a de Sitter wedge between two end-of-the-world branes is dual to a lower-dimensional conformal field theory, and shows by bulk computations in dS$_4$ that the dual's central charge is…

The reading

This paper tests the proposal known as DS wedge holography: that classical gravity in a de Sitter space cut into a wedge by two end-of-the-world branes is equivalent to a conformal field theory living on the $(d-2)$-dimensional corner where the branes meet. Working out the four-dimensional case in detail, the authors compute the partition function, pseudo entropy, pseudo-Renyi entropy, and scalar two-point functions from the bulk, and in every case recover the prediction of a two-dimensional CFT on a sphere, with imaginary central charge $c = i\, 3 l_{\mathrm{dS}}/(2G_3)$, signalling a non-unitary dual. They repeat the central charge extraction in a second, Euclidean-AdS slicing of the same wedge and obtain the same value, then analyse a limiting 'DS/dS band' geometry in which the branes no longer meet and the central charge becomes real. If the duality holds, these computations give concrete quantitative predictions for a two-dimensional non-unitary CFT that would describe a corner of four-dimensional de Sitter quantum gravity.

What carries the argument

The engine of the paper is the two-brane wedge construction. Two end-of-the-world branes sit at constant values of the slicing coordinate $w$ (Lorentzian case: branes carrying a $dS_{d-1}$ metric) or $\tau$ (Euclidean case: branes carrying an $EAdS_{d-1}$ metric) inside $dS_d$, with tensions fixed by Neumann boundary conditions; the wedge between them has an $S^{d-2}$ corner where the dual CFT lives, and generator counting — the branes remove $d$ of the $dS$ isometries — matches the CFT conformal group. The dictionary $Z_{CFT} \sim e^{i I_L - I_E}$ imports the no-boundary rule from dS/CFT: on-shell actions and extremal surfaces are computed in a Lorentzian part and a Euclidean hemisphere glued at $r = l_{\mathrm{dS}}$, and the entropy computation uses the two-step minimization formula of AdS wedge holography, in which a bulk surface is anchored on minimal surfaces living on the two branes. In the Euclidean slicing the workhorse is a separation-of-variables solution for a bulk scalar whose zero mode yields a massless brane field with profile $z K_\nu(kz)$, converting the bulk action into the CFT two-point function.

Extended reading notes

Core claim

In the paper's own terms, the core discovery is that the Codimension Two Holography Statement — classical gravity on $d$-dimensional de Sitter space inside a wedge between two EOW branes is dual to a $(d-2)$-dimensional CFT at the brane intersection — passes a battery of quantitative consistency checks in $dSW_4/CFT_2$. The partition function of the wedge, evaluated with the Lorentzian/Euclidean no-boundary action and compared with the holographic Weyl anomaly of a sphere CFT, yields $c = i\,3l_{\mathrm{dS}}/(2G_3)$; the same value recurs in the logarithmic term of the pseudo entropy, in the $n$-dependence of the pseudo-Renyi entropy, and in a completely different EAdS slicing of the same bulk. In that Euclidean slicing the bulk two-point function of a massless scalar reduces to the CFT$_2$ form $\langle O(x)O(y)\rangle \propto |x-y|^{-4}$ with an overall factor set by the brane separation. For the DS/dS band, where the Euclidean branes are nested latitude spheres that never meet, $\log Z$ equals the de Sitter entropy $S_{dS_3}$ and the central charge is real, so the wedge and band realizations of codimension-two holography differ in an explicit, computable way.

Load-bearing premise

The entire comparison rests on the assumption that the no-boundary extremal-surface prescription for a single de Sitter space — surfaces anchored on the future boundary of each $dS_{d-1}$ slice, with the Lorentzian part and Euclidean hemisphere glued at $r = l_{\mathrm{dS}}$, and the AdS-wedge two-step minimization — continues to hold inside the two-brane wedge unchanged; the paper invokes this as a 'similar procedure' in Section 3.2 without deriving it for the wedge geometry.

Editorial extensions

If this is right

  • If the $dSW_4/CFT_2$ dictionary holds, the universal quantities of the corner theory are fixed: entropy carries the imaginary log term with coefficient $l_{\mathrm{dS}}/(2G_3)$, and the real part from the Euclidean hemisphere equals exactly half the $dS_3$ de Sitter entropy.
  • The equal central charges from the Lorentzian and Euclidean slicings, $c = i\,3l_{\mathrm{dS}}/(2G_3)$ in both (3.8) and (4.25), mean the wedge's predictions do not depend on which way the bulk is cut.
  • The bulk two-point function fixes the scalar operator's dimension and normalization in the dual CFT: $\langle O(x)O(y)\rangle = -i(\cosh\tau_2 - \cosh\tau_1)(2l_{\mathrm{dS}}/\pi)|x-y|^{-4}$, with brane separation setting the overall factor.
  • The appendix-B replica computation extends the pattern to $dSW_5/CFT_3$: the imaginary part of the boundary Renyi entropy again matches the dS/CFT result in the $n \to 1$ limit.
  • Removing the branes (the $w_1 \to 0$, $w_2 \to \pi l_{\mathrm{dS}}$ limit) turns the wedge and band actions into the full-sphere action with $\log Z = S_{dS_d}$, recovering nested DS/dS and the standard de Sitter entropy.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the imaginary central charge is a property of the corner theory rather than an artifact of the no-boundary gluing rule, the wedge CFT is a non-unitary, timelike/coherent-state type theory, and the hemisphere's finite real contribution $\pi l_{\mathrm{dS}}/(4G_3)$ becomes a state-counting prediction worth testing against any microscopic dual.
  • The paper works in large-cutoff limits; computing the pseudo entropy at finite brane separation $(\tau_2 - \tau_1)$ would expose subleading terms that either confirm the wedge dynamics is doing the work or reveal that (3.29) is a kinematic replay of the $dS_3$ result.
  • The band realizes the same codimension-two idea with real $c = 3l_{\mathrm{dS}}/(2G_3)$; a construction interpolating between nested latitude spheres and meeting branes would clarify exactly where, and why, the central charge becomes imaginary.
Original abstract

Following \cite{Yadav:2024ray} we embark on a further study of the codimension two holography in de Sitter (dS) space. The $d$ dimensional bulk dS space is sliced by two end of the world $(d-1)$ dimensional branes which are bestowed with either Lorentzian dS or Euclidean AdS metric joining at a common $(d-2)$ dimensional space where the dual CFT lives. Through explicit computations of the holographic entanglement entropy, partition function, and Renyi entropy in both slicings for the bulk dS space emphasizing their similarities as well as differences we provide further evidence for this duality. We also make comments on further generalization of the codimension two holography.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-10-16: 1 request, 3,736 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.09 · human participants 0.01 · controlled comparison 0.10 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.68 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

Following \cite{Yadav:2024ray} we embark on a further study of the codimension two holography in de Sitter (dS) space. The $d$ dimensional bulk dS space is sliced by two end of the world $(d-1)$ dimensional branes which are bestowed with either Lorentzian dS or Euclidean AdS metric joining at a common $(d-2)$ dimensional space where the dual CFT lives. Through explicit computations of the holographic entanglement entropy, partition function, and Renyi entropy in both slicings for the bulk dS space emphasizing their similarities as well as differences we provide further evidence for this duality. We also make comments on further generalization of the codimension two holography.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Following \cite{Yadav:2024ray} we embark on a further study of the codimension two holography in de Sitter (dS) space. background 0.69 0.67 0.03 asserted 0.65
s1 The $d$ dimensional bulk dS space is sliced by two end of the world $(d-1)$ dimensional branes which are bestowed with either Lorentzian dS or Euclidean AdS metric joining at a common $(d-2)$ dimensional space where the dual CFT lives. method 0.43 0.18 0.07 asserted 0.99
s2 Through explicit computations of the holographic entanglement entropy, partition function, and Renyi entropy in both slicings for the bulk dS space emphasizing their similarities as well as differences we provide further evidence for this duality. contribution 0.83 0.95 0.65 asserted 0.89
s3 We also make comments on further generalization of the codimension two holography. future work 0.97 0.70 0.05 unclear 0.80

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.71.

What was examined, and what was not

sources read
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not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures
Figure 1. Wedge holography in de Sitter space as a bulk theory: dSWd/CF Td−2 wedge. Green and red curves denote EOW branes at w = w1 (Y1) and w = w2 (Y2). The dual CFT lives on Σ(S d−2 ) and is dual to de Sitter gravity in the wedge, dSW d. In this case, we have CFT on S 2 . The gravitational on shell action in four dimensions is given by simplifying eq.(2.18) for d = 4, which gives us I L dSW4 = 1 16πG3 Z dθdϕdτ sin(θ) cosh2  τ ldS  (6 − 2) = ldS G3 Z τ∞ 0 dτ cosh2  τ ldS  = ldS 2G3  τ∞ ldS + cosh τ∞ ldS  sinh τ∞ ldS  = ldS 8G3  4 τ∞ ldS + e 2
Figure 2. Cartoon of no boundary extremal surfaces in DS wedge holography. This is from the point of view of the wedge formed by Y1 and Y2; we have not shown the bulk extremal surface ΓA. The extremal surfaces from the hemisphere and Lorentzian parts are glued at r = ldS. Now, we discuss the explicit computation for three-dimensional de Sitter gravity on EOW branes, i.e., in dSW4/CF T2 correspondence. Since the no boundary geometry con￾sists of Lorentzian and hemisphere parts, we divide our discussion into two parts as follows. Lorentzian part: The metric for the constant t slice in the…
Figure 3. The DS/dS band. (a) Cross-section of Euclidean dSd ≃ S d . The EOW branes Y1 (green) and Y2 (red) are nested latitude spheres S d−1 . The band B (shaded) lies between them and there is no corner. The dotted vertical line is α = πldS/2. Its part inside the band (purple), S d−2 ×[w1, w2] contains the DS/dS central slices of all intermediate spheres where the (d − 2)-dimensional dual lives after reduction along w. (b) Brane removal limit w1 → 0, w2 → πldS: the band becomes all of S d and log Z = SdSd , eq. (C.13). 5 DS/dS band The bulk metric is ds2 = dw2 + sin2  w ldS  dα2 + l 2 dS…

Figures reproduced from arXiv:2610.22101 by the authors.

References

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