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REVIEW 2 major objections 5 minor 112 references

Holographic Correlators of Boundary/Crosscap CFTs in Two Dimensions

T0 review · 2 major / 5 minor · reviewed 2026-08-09 · deepseek-v4-flash

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Pith's one-line read Applying the GKPW dictionary to AdS3 with a Neumann end-of-the-world brane yields exact two- and three-point stress tensor correlators for BCFT2, and the same construction on a Z2 quotient of global AdS3 gives exact scalar and stress…

desk verdict A solid analytic tour de force for BCFT stress tensor correlators, with a more conditional RP2 crosscap section that needs a Ward identity check before I'd take its two-point functions at face value. read the letter →

arxiv 2501.18386 v2 pith:FFL6NBX5 submitted 2025-01-30 hep-th gr-qc

Yun-Ze Li , Yunfei Xie , Song He This is my paper · ORCID
classification hep-thgr-qc PACS 11.25.Tq11.25.Hf
keywords AdS/BCFTcrosscapCFTend-of-the-worldbranestresstensorcorrelatorsrealprojectiveplaneholographicrenormalizationT-TbardeformationGKPWrelation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper derives exact holographic correlators for two classes of two-dimensional CFTs with defects: boundary CFTs (BCFT2) and crosscap CFTs on the real projective plane (RP2). Working in semiclassical AdS3/CFT2, it computes two- and three-point stress tensor correlators in AdS3/BCFT2, derives recurrence relations for higher-point correlators, and shows that the two- and three-point functions are independent of the end-of-the-world brane tension. On the non-orientable side, it obtains exact scalar one- and two-point functions and stress tensor two-point functions on RP2 from a Z2 quotient of global AdS3 whose fixed-point singularity is resolved by a brane, and it also gives the finite-cutoff (T-Tbar deformed) versions of these correlators. The BCFT recurrence relations match the boundary Ward identities, and the heavy-operator limit of the RP2 one-point function matches the geodesic approximation, so the paper supplies concrete holographic predictions for CFTs on manifolds with boundaries and on non-orientable surfaces.

What carries the argument

The engine of the calculation is the GKPW relation, which equates the bulk on-shell gravitational action to the boundary CFT generating functional; in the semiclassical limit all correlators are functional derivatives of that action. The stress tensor computations use the Fefferman-Graham expansion of the bulk metric, whose first non-trivial coefficient g(2) encodes the Brown-York stress tensor, and the Neumann boundary condition (K_ij - K gamma_ij + T gamma_ij = 0) on the end-of-the-world brane, which determines the brane profile and relates it to the correlators. For the crosscap case the central object is the RP2 bulk saddle: global AdS3 quotiented by the antipodal map ($\theta$,phi) -> (pi-$\theta$, phi+pi), with the fixed point at eta=0 excised by an EOW brane of tension T<-1; scalar correlators follow from a Robin boundary condition on that brane and a spherical-harmonic decomposition restricted to even l, while stress tensor correlators follow from solving the perturbed Neumann condition on the sphere. At finite cutoff, the dictionary is the generalized GKPW relation for AdS3 truncated at z=z_c, whose dual is the T-Tbar deformed CFT (the solvable irrelevant deformation generated by the determinant of the stress tensor).

What would settle it

Evaluate the Euclidean on-shell actions of the proposed RP2 saddle (Z2 quotient of global AdS3 with fixed point at eta=0, resolved by an EOW brane of tension T<-1) and of the alternative smooth saddles for the same RP2 boundary, and check which has the lower action; the Section 3 correlators are only the answer if the proposed saddle dominates.

Watch

Extended reading notes

Core claim

The central claim is that the standard GKPW dictionary, applied to pure gravity in AdS3 with Neumann boundary conditions on an end-of-the-world brane, yields exact connected stress tensor correlators for BCFT2. Concretely, the paper obtains explicit two-point and three-point correlators for the tensionless brane, recurrence relations that generate higher-point correlators from lower-point ones, and a separate computation in hyperbolic slicing coordinates showing that general-tension two- and three-point correlators equal the tensionless ones. For crosscap CFT2, the claim is that the Z2 quotient of global AdS3 with antipodal identification fixed at the center, with the fixed-point singularity excised by an end-of-the-world brane of tension T<-1, is the holographic dual of the CFT on RP2; using it the paper computes exact scalar one- and two-point functions and stress tensor two-point functions, and shows the heavy-scalar one-point function agrees with the geodesic approximation. The same construction is then moved to a hard radial cutoff, giving deformed one- and two-point stress tensor correlators.

Load-bearing premise

For the RP2 results, the load-bearing premise is that the dominant bulk saddle is the Z2 quotient of global AdS3 whose antipodal identification has a fixed point at the center, with that singularity resolved by a single end-of-the-world brane of tension T<-1; the paper assumes this rather than proving it, and if another saddle contributes or the resolution differs, every crosscap correlator in Section 3 changes.

Editorial extensions

If this is right

  • If the BCFT results are correct, the recurrence relations (62)-(64) constitute a direct confirmation that the GKPW dictionary with a Neumann brane reproduces the boundary Ward identity structure of BCFT2.
  • Because the two- and three-point BCFT correlators do not depend on brane tension, tension-free calculations capture these boundary observables in AdS3/BCFT2, and tension only enters through the brane profile itself.
  • The RP2 scalar one- and two-point functions and stress tensor two-point functions become concrete holographic predictions for crosscap CFTs, with the heavy-dimension limit of the one-point function anchored by the geodesic approximation.
  • The finite-cutoff results give explicit T-Tbar-deformed versions of the RP2 stress tensor correlators, showing exactly how a hard radial cutoff deforms one- and two-point functions on the projective plane.
  • The explicit infinite-sum form of the RP2 scalar two-point function can be directly compared with boundary crosscap OPE data.

Reading between the lines

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

  • A natural extension the paper leaves implicit is the same Z2-quotient-plus-brane construction on the Klein bottle and on higher non-orientable surfaces; if the saddle-dominance assumption holds there, the method yields concrete Klein-bottle correlators that could be checked against known universal entropy results.
  • The demonstrated tension independence of BCFT two- and three-point correlators suggests a stronger conjecture: in AdS3/BCFT2 all higher-point stress tensor correlators, and possibly correlators involving boundary operators, are tension-independent; computing one four-point or boundary-operator correlator would test this.
  • The scalar two-point function (133) is an explicit infinite series over even spherical harmonics, so a direct boundary computation of the crosscap OPE, or a numerical simulation of a crosscap state in a lattice CFT, could check the coefficients A_l^(1) term by term.
  • If the finite-cutoff dictionary is exactly T-Tbar, the deformed RP2 one-point function should satisfy the T-Tbar flow equation in the large-central-charge limit, which is a concrete check of the cutoff construction beyond the correlators reported here.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 5 minor

Summary. The paper computes holographic stress tensor correlators in AdS3/BCFT2 for both tensionless and tensionful end-of-the-world branes, deriving explicit two- and three-point functions and recurrence relations. It then extends the holographic approach to two-dimensional crosscap CFTs on RP2, computing exact scalar one- and two-point functions, stress tensor two-point functions, and their finite-cutoff (TTbar-deformed) versions. The methodology follows standard GKPW holographic renormalization with Neumann boundary conditions on the EOW brane. The BCFT section is checked by matching two independent coordinate frames and by comparing recurrence relations to BCFT Ward identities. The heavy-dimension scalar one-point function is matched to a geodesic approximation. The RP2 results rely on the model of [56], in which the quotient singularity is resolved by a single EOW brane.

Significance. If the results are correct, the paper provides concrete holographic predictions for boundary and non-orientable CFTs in two dimensions, including explicit exact correlators that are not yet available from other methods. The BCFT part is a solid extension of earlier work and contains useful consistency checks. The crosscap part is novel and addresses an underdeveloped area, but its correctness hinges on the two-point function of the stress tensor on RP2, which is not independently verified. The paper is clearly written and the derivations are mostly unambiguous, but the RP2 stress tensor sector needs scrutiny.

major comments (2)
  1. [§3.3, Eq. (158)] The two-point function ⟨Tww(w)Tww(w')⟩ in Eq. (158) contains only the direct-channel pole (3/(16π²G)) (w−w')⁻⁴ and a contact term supported at the image point w = −1/\bar{w}'. The crosscap Ward identity, which follows from the involution w → −1/\bar{w}, requires a non-contact image-channel singularity at w = −1/\bar{w}' of the form (3/(16π²G)) (w + 1/\bar{w}')⁻⁴ (up to the appropriate tensor factor). This is also what one expects from the covering-space expression (156), which explicitly contains four singular terms, two at the direct point and two at the antipodal image. After the coordinate change (157), those image terms do not disappear; they should appear as a fourth-order pole at the image point. Its absence in (158) means either the conversion from (156) to (158) is incorrect, or (158) is incomplete. Since the later finite-cutoff results in §3.4 are built on this two-point function, this is a load-bearing issue.
  2. [§3.3] The RP2 stress tensor two-point functions are not checked against any independent CFT-side criterion. In the BCFT section, the recurrence relations are explicitly compared to the BCFT Ward identities (§2.2.2), and the scalar one-point function is checked against a geodesic approximation (§3.2). For the crosscap stress tensor, no analogous check is provided. I request that the authors verify that the final expressions, e.g. (158)–(161), satisfy the Ward identity associated with the crosscap involution, including the correct singular behaviour at the image point. This is necessary to exclude the possibility that the holographic computation missed an image contribution.
minor comments (5)
  1. [§3.1] The assumption that the dominant bulk saddle is the Z2 quotient of global AdS3 with a single EOW brane of tension T<−1 is clearly stated, but it is an assumption inherited from [56]. If other saddles contribute, the RP2 correlators would change. I suggest making this caveat more prominent, e.g., in the introduction or at the start of §3.
  2. [Eq. (90)] In several places, terms like "e−|ω(x−x0)|" should read "e^{−|ω|(x−x0)}"; the absolute value sign is missing on ω.
  3. [Eqs. (158)–(160)] The notation δ(2)(w + ¯w′−1) is confusing; I suggest writing δ^{(2)}(w + 1/\bar{w}') to make the support of the delta explicit.
  4. [§3.4, footnote 7] The assumption that the brane tension T does not flow with the cutoff is stated without discussion. A sentence justifying this, or at least pointing to a reference where it is discussed, would be helpful.
  5. [Various] The paper sometimes uses "correlators" without specifying connectedness; since Eq. (13) defines connected correlators, please be consistent in the terminology.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the correlators are computed from the GKPW dictionary with no fitted inputs, and the load-bearing RP2 saddle assumption is an explicit external input, not a self-referential reduction.

full rationale

The paper's derivation chain is self-contained in the relevant sense: every advertised correlator is obtained by solving the bulk equations with the stated boundary conditions and then differentiating the on-shell action via the GKPW relation, rather than by fitting a parameter to the output. In Section 2, the stress tensor two- and three-point functions follow from the Fefferman-Graham expansion, the Brown-York dictionary (13)-(14), and the Neumann condition (6); the brane tension T and the source perturbations are inputs, not quantities tuned to reproduce the final correlators. The recurrence relations (62)-(64) are derived from the linearized Einstein equations and the boundary condition (59), and only afterwards are they compared with the BCFT Ward identity, with the paper explicitly saying 'If we exclude the contact terms, these results align with the Ward identity in BCFT2'. This is a post-hoc check, not an input, so it does not make the derivation circular. In Section 3, the RP2 crosscap computation does rely on a specific bulk saddle, stated as 'we assume that the dominant saddle is constructed by the identification with a fixed point at eta = 0' and attributed to the external construction of reference [56]; that assumption is load-bearing but it is an explicit physical input from prior work by different authors, not a self-citation, and not an equation that is equivalent to the target correlators by definition. The scalar one-point function is independently checked against the geodesic approximation, and the stress tensor correlators are new outputs of the same holographic procedure. The self-citations [17-20] are contextual references to the authors' earlier torus and higher-genus computations and do not carry the argument. The skeptic's concern about the RP2 stress tensor two-point function and the crosscap Ward identity is a potential consistency or correctness issue, not a circularity, because no correlator is used as its own input. Overall, the paper shows no pattern of fitted inputs being renamed as predictions, no self-citation chain forcing the result, and no definitional equivalence between premises and conclusions.

Assumptions & free parameters 3 free parameters · 7 assumptions · 0 invented entities

No numbers are fitted to data; the central results are functions of model inputs T, lambda1, lambda2, and mu. The main axioms are the holographic dictionary, semiclassical saddle dominance, Neumann brane dynamics, the RP2 quotient construction of [56], and the regularity conditions used to fix homogeneous solutions. No new particles, forces, or degrees of freedom are introduced.

free parameters (3)
  • EOW brane tension T
    Input parameter of the AdS/BCFT and RP2 constructions, appearing via T = -k/sqrt(1+k^2) and eta* = arccoth(-T). It is not fitted. The BCFT two- and three-point correlators are shown to be independent of T.
  • Brane scalar couplings lambda1 and lambda2
    External couplings in the brane scalar action Eq. (117). They determine the Robin boundary condition (118) and appear in the scalar one- and two-point correlators.
  • TTbar deformation parameter mu (cutoff z_c)
    External finite-cutoff parameter with mu = 16*pi*G*z_c^2, Eq. (164). Results are given as functions of mu; no fitting to data is performed.
assumptions (7)
  • domain assumption The holographic GKPW dictionary equates the bulk on-shell action with the CFT generating functional.
    Used throughout via Eq. (12). Standard in AdS/CFT but unproved in this paper.
  • domain assumption The bulk path integral is dominated by a single classical saddle in the semiclassical limit.
    Stated at the start of Section 2. Needed to justify functional differentiation of a single on-shell action.
  • domain assumption The EOW brane satisfies the Neumann condition (K_ij - K gamma_ij + T gamma_ij)|_Q = 0 and its profile is fixed by this condition.
    Standard AdS/BCFT prescription from [23,24]. The entire brane-bending calculation rests on this assumption.
  • domain assumption For RP2, the dominant saddle is the Z2 quotient of global AdS3 with fixed point at eta=0, resolved by an EOW brane with T<-1.
    Taken from [56], Section 3.1. No proof of dominance or uniqueness is provided.
  • domain assumption Correlators and brane profiles are regular at x=0 and x=infinity, or at theta=0 and theta=pi, fixing homogeneous solutions.
    Used explicitly in Eqs. (29) and (89) to determine coefficients A and B. Without these conditions the two-point functions are not unique.
  • ad hoc to paper At finite cutoff, the brane tension T does not flow with the radial cutoff.
    Footnote 7 in Section 3.4: 'Here we assume that the brane tension T does not flow.' This assumption simplifies the deformed brane profile calculation.
  • domain assumption The scalar field is coupled to the EOW brane through the quadratic brane action Eq. (117), giving the Robin condition (118).
    A model choice from the brane-localized scalar literature; the scalar correlators depend on it.

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Cite this review

Pith. "Pith review of Holographic Correlators of Boundary/Crosscap CFTs in Two Dimensions." pith.science (2026). https://pith.science/paper/FFL6NBX5

@misc{pith2026250118386,
  author       = {Pith},
  title        = {Pith review of: Holographic Correlators of Boundary/Crosscap CFTs in Two Dimensions},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FFL6NBX5}},
  note         = {Machine review of arXiv:2501.18386}
}
abstract

This work explores holographic correlators within the frameworks of two-dimensional Boundary Conformal Field Theory (BCFT) and Crosscap Conformal Field Theory (XCFT). Utilizing the AdS/CFT correspondence, we compute stress tensor correlators in BCFT, considering both tensionless and tensionful end-of-the-world (EOW) brane scenarios. We derive recurrence relations for two-point and three-point correlators and examine the impact of non-zero brane tension on correlators. Extending these results, we investigate the holographic duals of XCFTs, presenting explicit scalar and stress tensor correlator computations on projective geometries such as $\mathbb{RP}^2$. Additionally, we analyze stress tensor correlators at a finite cutoff, uncovering deformations to one-point and two-point functions induced by the cutoff. Our findings provide novel insights into the holographic structures of BCFT and XCFT while laying the groundwork for future research into higher-dimensional extensions.

Figures

Figures reproduced from arXiv: 2501.18386 by the authors.

Figure 1
Figure 1. A sketch of Poincare AdS3 coordinates (left) and hyperbolic slicing coordinates (right). After the boundary metric perturbation (19), the coordinate transformation (65) more stress tensor insertions. 16 [PITH_FULL_IMAGE:figures/full_fig_p017_1.png] view at source ↗
Figure 2
Figure 2. An illustration of the holographic dual of XCFT [PITH_FULL_IMAGE:figures/full_fig_p028_2.png] view at source ↗

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Reference graph

Works this paper leans on

112 extracted references · 18 canonical work pages

  1. [56]

    Wei, Holographic Dual of Crosscap Conformal Field Theory , 2405.03755

    Z. Wei, Holographic Dual of Crosscap Conformal Field Theory , 2405.03755

    arXiv

  2. [1]

    J. M. Maldacena, The Large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231–252, [ hep-th/9711200]

    arXiv 1998

  3. [2]

    S. S. Gubser, I. R. Klebanov and A. M. Polyakov, Gauge theory correlators from noncritical string theory , Phys. Lett. B 428 (1998) 105–114, [hep-th/9802109]. 41

    arXiv 1998

  4. [3]

    Witten, Anti-de Sitter space and holography , Adv

    E. Witten, Anti-de Sitter space and holography , Adv. Theor. Math. Phys. 2 (1998) 253–291, [ hep-th/9802150]

    arXiv 1998

  5. [4]

    Aharony, S

    O. Aharony, S. S. Gubser, J. M. Maldacena, H. Ooguri and Y. Oz , Large N field theories, string theory and gravity , Phys. Rept. 323 (2000) 183–386, [hep-th/9905111]

    arXiv 2000

  6. [5]

    ’t Hooft, Dimensional reduction in quantum gravity , Conf

    G. ’t Hooft, Dimensional reduction in quantum gravity , Conf. Proc. C 930308 (1993) 284–296, [ gr-qc/9310026]

    arXiv 1993

  7. [6]

    Susskind, The World as a hologram , J

    L. Susskind, The World as a hologram , J. Math. Phys. 36 (1995) 6377–6396, [hep-th/9409089]

    arXiv 1995

  8. [7]

    A. B. Zamolodchikov, Irreversibility of the Flux of the Renormalization Group in a 2D Field Theory , JETP Lett. 43 (1986) 730–732

    1986

Show all 112 references
  1. [8]

    Liu and A

    H. Liu and A. A. Tseytlin, On four point functions in the CFT / AdS correspondence, Phys. Rev. D 59 (1999) 086002, [ hep-th/9807097]

    1999 arXiv

  2. [9]

    Arutyunov and S

    G. Arutyunov and S. Frolov, Three point Green function of the stress energy tensor in the AdS / CFT correspondence , Phys. Rev. D 60 (1999) 026004, [hep-th/9901121]

    1999 arXiv

  3. [10]

    D’Hoker, D

    E. D’Hoker, D. Z. Freedman, S. D. Mathur, A. Matusis and L. Ra stelli, Graviton and gauge boson propagators in AdS(d+1) , Nucl. Phys. B 562 (1999) 330–352, [ hep-th/9902042]

    1999 arXiv

  4. [11]

    Bianchi, D

    M. Bianchi, D. Z. Freedman and K. Skenderis, How to go with an RG flow , JHEP 08 (2001) 041, [ hep-th/0105276]

    2001 arXiv

  5. [12]

    Bianchi, D

    M. Bianchi, D. Z. Freedman and K. Skenderis, Holographic renormalization, Nucl. Phys. B 631 (2002) 159–194, [ hep-th/0112119]

    2002 arXiv

  6. [13]

    Papadimitriou and K

    I. Papadimitriou and K. Skenderis, Correlation functions in holographic RG flows, JHEP 10 (2004) 075, [ hep-th/0407071]

    2004 arXiv

  7. [14]

    Raju, Four Point Functions of the Stress Tensor and Conserved Curr ents in AdS 4/CFT3, Phys

    S. Raju, Four Point Functions of the Stress Tensor and Conserved Curr ents in AdS 4/CFT3, Phys. Rev. D 85 (2012) 126008, [ 1201.6452]. 42

    2012 arXiv

  8. [15]

    Bagchi, D

    A. Bagchi, D. Grumiller and W. Merbis, Stress tensor correlators in three-dimensional gravity, Phys. Rev. D 93 (2016) 061502, [ 1507.05620]

    2016 arXiv

  9. [16]

    Nguyen, Holographic boundary actions in AdS 3/CFT2 revisited, JHEP 10 (2021) 218, [ 2108.01095]

    K. Nguyen, Holographic boundary actions in AdS 3/CFT2 revisited, JHEP 10 (2021) 218, [ 2108.01095]

    2021 arXiv

  10. [17]

    S. He, Y. Li, Y.-Z. Li and Y. Zhang, Holographic torus correlators of stress tensor in AdS 3/CFT2, JHEP 06 (2023) 116, [ 2303.13280]

    2023 arXiv

  11. [18]

    He, Y.-Z

    S. He, Y.-Z. Li and Y. Zhang, Holographic torus correlators in AdS 3 gravity coupled to scalar field , JHEP 05 (2024) 254, [ 2311.09636]

    2024 arXiv

  12. [19]

    S. He, Y. Li, Y.-Z. Li and Y. Zhang, Note on holographic torus stress tensor correlators in AdS 3 gravity, JHEP 09 (2024) 125, [ 2405.01255]

    2024 arXiv

  13. [20]

    He, Y.-Z

    S. He, Y.-Z. Li and Y. Xie, Holographic stress tensor correlators on higher genus Riemann surfaces , JHEP 10 (2024) 208, [ 2406.04042]

    2024 arXiv

  14. [21]

    He and Y

    S. He and Y. Li, Holographic Euclidean thermal correlator , 2308.13518

    arXiv

  15. [22]

    Karch and L

    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]

    2001 arXiv

  16. [23]

    Takayanagi, Holographic Dual of BCFT , Phys

    T. Takayanagi, Holographic Dual of BCFT , Phys. Rev. Lett. 107 (2011) 101602, [ 1105.5165]

    2011 arXiv

  17. [24]

    Fujita, T

    M. Fujita, T. Takayanagi and E. Tonni, Aspects of AdS/BCFT , JHEP 11 (2011) 043, [ 1108.5152]

    2011 arXiv

  18. [25]

    Nozaki, T

    M. Nozaki, T. Takayanagi and T. Ugajin, Central Charges for BCFTs and Holography, JHEP 06 (2012) 066, [ 1205.1573]

    2012 arXiv

  19. [26]

    Miao, Holographic BCFT with Dirichlet Boundary Condition , JHEP 02 (2019) 025, [ 1806.10777]

    R.-X. Miao, Holographic BCFT with Dirichlet Boundary Condition , JHEP 02 (2019) 025, [ 1806.10777]

    2019 arXiv

  20. [27]

    Guijosa, Y

    A. Guijosa, Y. D. Olivas and J. F. Pedraza, Holographic coarse-graining: correlators from the entanglement wedge and other reduced g eometries, JHEP 08 (2022) 118, [ 2201.01786]. 43

    2022 arXiv

  21. [28]

    Miao, C.-S

    R.-X. Miao, C.-S. Chu and W.-Z. Guo, New proposal for a holographic boundary conformal field theory , Phys. Rev. D 96 (2017) 046005, [1701.04275]

    2017 arXiv

  22. [29]

    Chu, R.-X

    C.-S. Chu, R.-X. Miao and W.-Z. Guo, On New Proposal for Holographic BCFT, JHEP 04 (2017) 089, [ 1701.07202]

    2017 arXiv

  23. [30]

    Ryu and T

    S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602, [ hep-th/0603001]

    2006 arXiv

  24. [31]

    Ryu and T

    S. Ryu and T. Takayanagi, Aspects of Holographic Entanglement Entropy , JHEP 08 (2006) 045, [ hep-th/0605073]

    2006 arXiv

  25. [32]

    V. E. Hubeny, M. Rangamani and T. Takayanagi, A Covariant holographic entanglement entropy proposal , JHEP 07 (2007) 062, [ 0705.0016]

    2007 arXiv

  26. [33]

    Alishahiha and R

    M. Alishahiha and R. Fareghbal, Boundary CFT from Holography , Phys. Rev. D 84 (2011) 106002, [ 1108.5607]

    2011 arXiv

  27. [34]

    M. R. Setare and V. Kamali, Anti–de Sitter/ boundary conformal field theory correspondence in the nonrelativistic limit , Eur. Phys. J. C 72 (2012) 2115, [1202.4917]

    2012 arXiv

  28. [35]

    Hinterbichler, J

    K. Hinterbichler, J. Stokes and M. Trodden, Holographic CFTs on maximally symmetric spaces: correlators, integral transforms and ap plications, Phys. Rev. D 92 (2015) 065025, [ 1505.05513]

    2015 arXiv

  29. [36]

    Kastikainen and S

    J. Kastikainen and S. Shashi, Structure of holographic BCFT correlators from geodesics, Phys. Rev. D 105 (2022) 046007, [ 2109.00079]

    2022 arXiv

  30. [37]

    Park, Correlation functions of boundary and defect conformal fiel d theories, Phys

    C. Park, Correlation functions of boundary and defect conformal fiel d theories, Phys. Rev. D 110 (2024) 046010, [ 2405.15108]

    2024 arXiv

  31. [38]

    J. Tian, T. Lai and F. Omidi, Spacetime Bananas with EOW Branes and Spins, 2410.18729

  32. [39]

    Izumi, T

    K. Izumi, T. Shiromizu, K. Suzuki, T. Takayanagi and N. Tanaha shi, Brane dynamics of holographic BCFTs , JHEP 10 (2022) 050, [ 2205.15500]. 44

    2022 arXiv

  33. [40]

    Suzuki and S

    Y.-k. Suzuki and S. Terashima, On the dynamics in the AdS/BCFT correspondence, JHEP 09 (2022) 103, [ 2205.10600]

    2022 arXiv

  34. [41]

    J. L. Cardy, Conformal Invariance and Surface Critical Behavior , Nucl. Phys. B 240 (1984) 514–532

    1984

  35. [42]

    J. L. Cardy, Boundary conformal field theory , hep-th/0411189

    arXiv

  36. [43]

    C. P. Burgess and T. R. Morris, Open and Unoriented Strings a La Polyakov , Nucl. Phys. B 291 (1987) 256–284

    1987

  37. [44]

    Ishibashi, The Boundary and Crosscap States in Conformal Field Theories, Mod

    N. Ishibashi, The Boundary and Crosscap States in Conformal Field Theories, Mod. Phys. Lett. A 4 (1989) 251

    1989

  38. [45]

    Fioravanti, G

    D. Fioravanti, G. Pradisi and A. Sagnotti, Sewing constraints and nonorientable open strings , Phys. Lett. B 321 (1994) 349–354, [hep-th/9311183]

    1994 arXiv

  39. [46]

    Pradisi, A

    G. Pradisi, A. Sagnotti and Y. S. Stanev, The Open descendants of nondiagonal SU(2) WZW models , Phys. Lett. B 356 (1995) 230–238, [hep-th/9506014]

    1995 arXiv

  40. [47]

    Giombi, H

    S. Giombi, H. Khanchandani and X. Zhou, Aspects of CFTs on Real Projective Space, J. Phys. A 54 (2021) 024003, [ 2009.03290]

    2021 arXiv

  41. [48]

    Tsiares, Universal Dynamics in Non-Orientable CFT 2, 2011.09250

    I. Tsiares, Universal Dynamics in Non-Orientable CFT 2, 2011.09250

    2011 arXiv

  42. [49]

    B.-Y. Tan, Y. Zhang, H.-C. Zhang, W. Tang, L. Wang, H.-H. Tu et al., Extracting the Luttinger Parameter from a Single Wave Funct ion, Phys. Rev. Lett. 134 (2025) 076501, [ 2402.18364]

    2025 arXiv

  43. [50]

    Zhang, Y.-H

    Y. Zhang, Y.-H. Wu, L. Wang and H.-H. Tu, Crosscap states and duality of Ising field theory in two dimensions , 2409.11046

  44. [51]

    Verlinde, Poking Holes in AdS/CFT: Bulk Fields from Boundary States , 1505.05069

    H. Verlinde, Poking Holes in AdS/CFT: Bulk Fields from Boundary States , 1505.05069. 45

    arXiv

  45. [52]

    Nakayama and H

    Y. Nakayama and H. Ooguri, Bulk Local States and Crosscaps in Holographic CFT, JHEP 10 (2016) 085, [ 1605.00334]

    2016 arXiv

  46. [53]

    Lewkowycz, G

    A. Lewkowycz, G. J. Turiaci and H. Verlinde, A CFT Perspective on Gravitational Dressing and Bulk Locality , JHEP 01 (2017) 004, [1608.08977]

    2017 arXiv

  47. [54]

    Maloney and S

    A. Maloney and S. F. Ross, Holography on Non-Orientable Surfaces , Class. Quant. Grav. 33 (2016) 185006, [ 1603.04426]

    2016 arXiv

  48. [55]

    Caetano and L

    J. Caetano and L. Rastelli, Holography for N = 4 on /CA/C8 4, JHEP 02 (2023) 106, [ 2206.06375]

    2023 arXiv

  49. [57]

    Wei and Y

    Z. Wei and Y. Yoneta, Crosscap Quenches and Entanglement Evolution , 2412.18610

    arXiv

  50. [58]

    G. W. Gibbons and S. W. Hawking, Action Integrals and Partition Functions in Quantum Gravity , Phys. Rev. D 15 (1977) 2752–2756

    1977

  51. [59]

    de Haro, S

    S. de Haro, S. N. Solodukhin and K. Skenderis, Holographic reconstruction of space-time and renormalization in the AdS / CFT corresponde nce, Commun. Math. Phys. 217 (2001) 595–622, [ hep-th/0002230]

    2001 arXiv

  52. [60]

    Henningson and K

    M. Henningson and K. Skenderis, The Holographic Weyl anomaly , JHEP 07 (1998) 023, [ hep-th/9806087]

    1998 arXiv

  53. [61]

    Skenderis, Lecture notes on holographic renormalization , Class

    K. Skenderis, Lecture notes on holographic renormalization , Class. Quant. Grav. 19 (2002) 5849–5876, [ hep-th/0209067]

    2002 arXiv

  54. [62]

    Balasubramanian and P

    V. Balasubramanian and P. Kraus, A Stress tensor for Anti-de Sitter gravity , Commun. Math. Phys. 208 (1999) 413–428, [ hep-th/9902121]

    1999 arXiv

  55. [63]

    Emparan, C

    R. Emparan, C. V. Johnson and R. C. Myers, Surface terms as counterterms in the AdS / CFT correspondence , Phys. Rev. D 60 (1999) 104001, [hep-th/9903238]. 46

    1999 arXiv

  56. [64]

    Kraus, F

    P. Kraus, F. Larsen and R. Siebelink, The gravitational action in asymptotically AdS and flat space-times , Nucl. Phys. B 563 (1999) 259–278, [hep-th/9906127]

    1999 arXiv

  57. [65]

    Fefferman and C

    C. Fefferman and C. R. Graham, Conformal invariants , Ast´ erisqueS131 (1985)

    1985

  58. [66]

    Fefferman and C

    C. Fefferman and C. R. Graham, The ambient metric , Ann. Math. Stud. 178 (2011) 1–128, [ 0710.0919]

    2011 arXiv

  59. [67]

    Banados, Three-dimensional quantum geometry and black holes , AIP Conf

    M. Banados, Three-dimensional quantum geometry and black holes , AIP Conf. Proc. 484 (1999) 147–169, [ hep-th/9901148]

    1999 arXiv

  60. [68]

    Skenderis and S

    K. Skenderis and S. N. Solodukhin, Quantum effective action from the AdS / CFT correspondence, Phys. Lett. B 472 (2000) 316–322, [ hep-th/9910023]

    2000 arXiv

  61. [69]

    J. D. Brown and J. W. York, Jr., Quasilocal energy and conserved charges derived from the gravitational action , Phys. Rev. D 47 (1993) 1407–1419, [gr-qc/9209012]

    1993 arXiv

  62. [70]

    J. D. Brown and M. Henneaux, Central Charges in the Canonical Realization of Asymptotic Symmetries: An Example from Three-Dimension al Gravity, Commun. Math. Phys. 104 (1986) 207–226

    1986

  63. [71]

    M. M. Roberts, Time evolution of entanglement entropy from a pulse , JHEP 12 (2012) 027, [ 1204.1982]

    2012 arXiv

  64. [72]

    D. M. McAvity and H. Osborn, Energy momentum tensor in conformal field theories near a boundary , Nucl. Phys. B 406 (1993) 655–680, [hep-th/9302068]

    1993 arXiv

  65. [73]

    L.-Y. Hung, R. C. Myers and M. Smolkin, Some Calculable Contributions to Holographic Entanglement Entropy , JHEP 08 (2011) 039, [ 1105.6055]

    2011 arXiv

  66. [74]

    Breitenlohner and D

    P. Breitenlohner and D. Z. Freedman, Positive Energy in anti-De Sitter Backgrounds and Gauged Extended Supergravity , Phys. Lett. B 115 (1982) 197–201. 47

    1982

  67. [75]

    Breitenlohner and D

    P. Breitenlohner and D. Z. Freedman, Stability in Gauged Extended Supergravity, Annals Phys. 144 (1982) 249

    1982

  68. [76]

    D. M. McAvity and H. Osborn, Quantum field theories on manifolds with curved boundaries: Scalar fields , Nuclear Physics B 394 (1993) 728–788

    1993

  69. [77]

    Abramowitz and I

    M. Abramowitz and I. A. Stegun, Handbook of mathematical functions with formulas, graphs, and mathematical tables , vol. 55. US Government printing office, 1968

    1968

  70. [78]

    McGough, M

    L. McGough, M. Mezei and H. Verlinde, Moving the CFT into the bulk with TT , JHEP 04 (2018) 010, [ 1611.03470]

    2018 arXiv

  71. [79]

    Hartman, J

    T. Hartman, J. Kruthoff, E. Shaghoulian and A. Tajdini, Holography at finite cutoff with a T 2 deformation, JHEP 03 (2019) 004, [ 1807.11401]

    2019 arXiv

  72. [80]

    A. B. Zamolodchikov, Expectation value of composite field T anti-T in two-dimensional quantum field theory , hep-th/0401146

    arXiv

  73. [81]

    F. A. Smirnov and A. B. Zamolodchikov, On space of integrable quantum field theories , Nucl. Phys. B 915 (2017) 363–383, [ 1608.05499]

    2017 arXiv

  74. [82]

    Tian, On-shell action of T ¯T-deformed Holographic CFTs , 2306.01258

    J. Tian, On-shell action of T ¯T-deformed Holographic CFTs , 2306.01258

    arXiv

  75. [83]

    Li, Comments on large central charge T ¯T deformed conformal field theory and cutoff AdS holography , 2012.14414

    Y. Li, Comments on large central charge T ¯T deformed conformal field theory and cutoff AdS holography , 2012.14414

    2012 arXiv

  76. [84]

    Guica and R

    M. Guica and R. Monten, T ¯T and the mirage of a bulk cutoff , SciPost Phys. 10 (2021) 024, [ 1906.11251]

    2021 arXiv

  77. [85]

    Li and Y

    Y. Li and Y. Zhou, Cutoff AdS 3 versus TT CFT2 in the large central charge sector: correlators of energy-momentum tensor , JHEP 12 (2020) 168, [2005.01693]

    2020 arXiv

  78. [86]

    H. Geng, S. L¨ ust, R. K. Mishra and D. Wakeham, Holographic BCFTs and Communicating Black Holes , jhep 08 (2021) 003, [ 2104.07039]. 48

    2021 arXiv

  79. [87]

    Kawamoto, T

    T. Kawamoto, T. Mori, Y.-k. Suzuki, T. Takayanagi and T. Ugaj in, Holographic local operator quenches in BCFTs , JHEP 05 (2022) 060, [2203.03851]

    2022 arXiv

  80. [88]

    Kusuki, Analytic bootstrap in 2D boundary conformal field theory: towards braneworld holography , JHEP 03 (2022) 161, [ 2112.10984]

    Y. Kusuki, Analytic bootstrap in 2D boundary conformal field theory: towards braneworld holography , JHEP 03 (2022) 161, [ 2112.10984]

    2022 arXiv

  81. [89]

    Kusuki, Semiclassical gravity from averaged boundaries in two-dimensional boundary conformal field theories , Phys

    Y. Kusuki, Semiclassical gravity from averaged boundaries in two-dimensional boundary conformal field theories , Phys. Rev. D 106 (2022) 066020, [ 2206.03035]

    2022 arXiv

  82. [90]

    Kusuki, Reflected entropy in boundary and interface conformal field theory, Phys

    Y. Kusuki, Reflected entropy in boundary and interface conformal field theory, Phys. Rev. D 106 (2022) 066009, [ 2206.04630]

    2022 arXiv

  83. [91]

    Miyaji and C

    M. Miyaji and C. Murdia, Holographic BCFT with a Defect on the End-of-the-World brane , JHEP 11 (2022) 123, [ 2208.13783]

    2022 arXiv

  84. [92]

    Biswas, J

    S. Biswas, J. Kastikainen, S. Shashi and J. Sully, Holographic BCFT spectra from brane mergers , JHEP 11 (2022) 158, [ 2209.11227]

    2022 arXiv

  85. [93]

    Kusuki and Z

    Y. Kusuki and Z. Wei, AdS/BCFT from conformal bootstrap: construction of gravity with branes and particles , JHEP 01 (2023) 108, [ 2210.03107]

    2023 arXiv

  86. [94]

    D. Bak, M. Gutperle and S. Hirano, A Dilatonic deformation of AdS(5) and its field theory dual , JHEP 05 (2003) 072, [ hep-th/0304129]

    2003 arXiv

  87. [95]

    D. Z. Freedman, C. Nunez, M. Schnabl and K. Skenderis, Fake supergravity and domain wall stability , Phys. Rev. D 69 (2004) 104027, [hep-th/0312055]

    2004 arXiv

  88. [96]

    D. Bak, M. Gutperle and S. Hirano, Three dimensional Janus and time-dependent black holes , JHEP 02 (2007) 068, [ hep-th/0701108]

    2007 arXiv

  89. [97]

    Chiodaroli, M

    M. Chiodaroli, M. Gutperle and D. Krym, Half-BPS Solutions locally asymptotic to AdS(3) x S**3 and interface conformal field the ories, JHEP 02 (2010) 066, [ 0910.0466]. 49

    2010 arXiv

  90. [98]

    D. Bak, M. Gutperle and R. A. Janik, Janus Black Holes , JHEP 10 (2011) 056, [ 1109.2736]

    2011 arXiv

  91. [99]

    Chiodaroli, J

    M. Chiodaroli, J. Estes and Y. Korovin, Holographic two-point functions for Janus interfaces in the D1/D5 CFT, JHEP 04 (2017) 145, [ 1612.08916]

    2017 arXiv

  92. [100]

    Auzzi, S

    R. Auzzi, S. Baiguera, S. Bonansea, G. Nardelli and K. Toccac elo, Volume complexity for Janus AdS 3 geometries, JHEP 08 (2021) 045, [ 2105.08729]

    2021 arXiv

  93. [101]

    Suzuki and T

    K. Suzuki and T. Takayanagi, BCFT and Islands in two dimensions , JHEP 06 (2022) 095, [ 2202.08462]

    2022 arXiv

  94. [102]

    Erdmenger, M

    J. Erdmenger, M. Flory and M.-N. Newrzella, Bending branes for DCFT in two dimensions , JHEP 01 (2015) 058, [ 1410.7811]

    2015 arXiv

  95. [103]

    Kanda, M

    H. Kanda, M. Sato, Y.-k. Suzuki, T. Takayanagi and Z. Wei, AdS/BCFT with brane-localized scalar field , JHEP 03 (2023) 105, [ 2302.03895]

    2023 arXiv

  96. [104]

    Liu, H.-D

    Y. Liu, H.-D. Lyu and C.-Y. Wang, On AdS 3/ICFT2 with a dynamical scalar field located on the brane , JHEP 10 (2024) 001, [ 2403.20102]

    2024 arXiv

  97. [105]

    Fujiki, H

    K. Fujiki, H. Kanda, M. Kohara and T. Takayanagi, Brane Cosmology from AdS/BCFT, 2501.05036

    arXiv

  98. [106]

    F. Deng, Z. Wang and Y. Zhou, End of the world brane meets TT , JHEP 07 (2024) 036, [ 2310.15031]

    2024 arXiv

  99. [107]

    Deng and Z

    F. Deng and Z. Wang, Holographic boundary conformal field theory with T ¯T deformation, 2411.06345

    arXiv

  100. [108]

    D. Basu, H. Chourasiya, A. Dey and V. Raj, Bridging Boundaries: T ¯T , Double Holography, and Reflected Entropy , 2411.12827

    arXiv

  101. [109]

    Louko and D

    J. Louko and D. Marolf, Single exterior black holes and the AdS / CFT conjecture, Phys. Rev. D 59 (1999) 066002, [ hep-th/9808081]

    1999 arXiv

  102. [110]

    Tu, Universal entropy of conformal critical theories on a Klein bottle, Phys

    H.-H. Tu, Universal entropy of conformal critical theories on a Klein bottle, Phys. Rev. Lett. 119 (2017) 261603, [ 1707.05812]. 50

    2017 arXiv

  103. [111]

    Zhang, A

    Y. Zhang, A. Hulsch, H.-C. Zhang, W. Tang, L. Wang and H.-H. T u, Universal Scaling of Klein Bottle Entropy near Conformal Cr itical Points, Phys. Rev. Lett. 130 (2023) 151602, [ 2211.09745]

    2023 arXiv

  104. [112]

    Pathak and L

    S. Pathak and L. K. Kovalsky, Non-Orientable AdS 3 and its Holography , 2404.12546. 51

    arXiv

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