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Surface growth scheme for bulk reconstruction and $T\bar T$ deformation

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Pith's one-line read This paper claims that the iterative radial growth of bulk minimal surfaces in asymptotically AdS spacetime is driven by the same operator flow as the T\bar T deformation of the boundary CFT, with the deformation parameter playing the…

desk verdict A real tensor-network extension and a correct-looking BTZ check sit on top of a central mapping that is assumed, not derived; the paper's headline claim is currently an ansatz. read the letter →

arxiv 2507.18435 v1 pith:SXCN4FTS submitted 2025-07-24 hep-th gr-qc

Hao-Chun Liang , Jia-Rui Sun , Yuan Sun This is my paper · ORCID
classification hep-thgr-qc PACS 11.25.Tq
keywords TTbardeformationsurfacegrowthschemebulkreconstructiontensornetworkentanglementdistillationAdS/CFTcorrespondenceholographicentropy
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

The paper tries to establish a dynamical identity: the layer-by-layer growth of homogeneous, isotropic bulk minimal surfaces in asymptotically AdS spacetime — the 'surface growth scheme' for reconstructing the bulk from boundary entanglement — is the holographic image of the T\bar T deformation flow of the boundary CFT2. If true, this gives T\bar T deformation a concrete geometric meaning as the engine that drives surface growth, and it turns the radial direction of AdS into the deformation parameter of the field theory. The authors argue via a generalized one-shot entanglement distillation tensor network whose continuum limit yields a unitary evolution and show that the surface metric operator and the traceless stress-tensor operator obey exactly the T\bar T flow equations under this evolution. The payoff would be a bottom-up mechanism for bulk gravitational dynamics: the coarse-graining operator of the tensor network acts as the deformation generator, so gravity in the bulk is reconstructed from the renormalization-group-like flow of the boundary theory.

What carries the argument

The central machinery is the generalized one-shot entanglement distillation (OSED) tensor network, extended so that each new layer of bulk minimal surfaces anchors on the turning points of the previous layer rather than on the boundary. In the continuum limit $N\to\infty$ the layer transitions are replaced by a unitary evolution operator $U(\mu,0)=P\exp(-i\int_0^\mu A(x)\,dx)$ acting on the surface-horizon Hilbert space, and the load-bearing operators are the surface metric $\gamma_{ab}$ and the traceless stress tensor $\hat{T}_{ab}$, whose Heisenberg evolution is assumed to obey the T\bar T flow equations. The coarse-graining operator $Q$, extracted from $A(x)$ via $A=K+Q$, plays the role of the deformation generator: its commutators with $\gamma_{ab}$ and $\hat{T}_{ab}$ reproduce the flow, encoding bulk diffeomorphism invariance. Matching the Fefferman-Graham expansion of asymptotically AdS3 with the mixed-boundary-condition formulation of T\bar T deformation fixes the identification $\rho_c=-\mu/C$ between radial cutoff and deformation parameter.

What would settle it

Extract the isometric transition between two layers from an explicit BTZ surface-growth network, compute the commutator $[Q,\gamma_{ab}]$ directly from the tensor data, and check whether $U^\dagger\gamma_{ab}U$ equals $\gamma_{ab}-2\mu\hat{T}_{ab}+\mu^2\hat{T}_{ac}\gamma^{cd}\hat{T}_{db}$ through second order in the layer spacing; a discrepancy in the $\mu^2$ coefficient would falsify the claimed equivalence.

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Extended reading notes

Core claim

The paper's central claim is that the iterative growth of homogeneous and isotropic bulk minimal surfaces in asymptotically AdS spacetime maps exactly onto the T\bar T operator flow of a boundary CFT2. Using the generalized OSED tensor network, the authors replace the discrete layer index with a continuous radial parameter $\mu$, and define metric and stress-tensor operators $\gamma_{ab}$ and $\hat{T}_{ab}$ whose expectation values at radius $\mu$ reproduce the T\bar T-deformed flow equations $\gamma_{ab}(\mu)=\gamma^{(0)}_{ab}-2\mu\hat{T}^{(0)}_{ab}+\mu^2\hat{T}^{(0)}_{ac}\gamma^{cd}_{(0)}\hat{T}^{(0)}_{db}$ and $\hat{T}_{ab}(\mu)=\hat{T}^{(0)}_{ab}-\mu\hat{T}^{(0)}_{ac}\gamma^{cd}_{(0)}\hat{T}^{(0)}_{db}$. They identify the coarse-graining isometry $Q$ in the tensor network as the generator of this flow, with the commutator structure $i[Q,\mathcal{O}]\sim \partial_\mu\langle\mathcal{O}\rangle_\mu$, so that bulk diffeomorphism invariance is encoded in the deformation. Consequently, T\bar T deformation supplies the dynamical mechanism for surface growth, and the radial evolution of the bulk is a field-theoretic renormalization-group flow.

Load-bearing premise

The argument rests on taking for granted that the layer-to-layer unitary evolution acts on the surface metric and stress-tensor operators exactly as the T\bar T flow equations prescribe, an equality that is assumed rather than derived from the tensor network.

Editorial extensions

If this is right

  • The radial direction of asymptotically AdS3 is not merely analogous to the T\bar T deformation parameter; layer-by-layer surface growth is literally the deformation flow, so reconstructing the bulk by surface growth is equivalent to running the T\bar T flow of the boundary theory.
  • The coarse-graining operator of the tensor network functions as the generator of the deformation, so bulk diffeomorphism invariance emerges from the commutator structure $i[Q,\mathcal{O}]\sim\partial_\mu\langle\mathcal{O}\rangle_\mu$.
  • In the continuum limit, surface growth from a cutoff surface $r_0$ to the horizon $r_h$ corresponds to the T\bar T flow from $\mu=0$ to $\mu=\mu_h$, linking the monotone decrease of surface entropy $S^{(k)}$ to the flow of the deformed CFT.
  • The framework yields a concrete realization of the surface/state correspondence: states on radial cutoff surfaces are T\bar T-deformed CFT states, and the horizon is reached at the endpoint of the flow.

Reading between the lines

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

  • If the map survives closer scrutiny, the same tensor network should reproduce the T\bar T-deformed entanglement entropy and R\'enyi entropy of boundary intervals directly from surface growth, giving an independent check beyond the operator flow.
  • The identification suggests that T\bar T deformation is not an exotic modification but the natural boundary dual of the simplest radial renormalization of holographic entanglement; other irrelevant deformations with the same flow structure might admit analogous geometric realizations.
  • One could probe the robustness of the claim by extending the construction to inhomogeneous or anisotropic surface growth, where the Fefferman-Graham expansion does not truncate, and asking whether a generalized flow still matches the surface dynamics.
  • The unitary evolution along the radial direction might be reinterpreted as a quantum channel for entanglement distillation, with the coarse-graining operator describing optimal distillation of the boundary state layer by layer.
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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

4 major / 5 minor

Summary. This paper proposes a connection between the surface growth scheme for bulk reconstruction and T\bar{T}-deformed CFT. It extends the one-shot entanglement distillation (OSED) tensor network to a general surface growth process, argues that the entanglement entropy of grown surfaces decreases monotonically and converges to the horizon entropy, computes the radial evolution of homogeneous isotropic surfaces in BTZ spacetime, and then claims that the continuum radial flow is generated by the T\bar{T} operator, with a coarse-graining operator Q playing the role of the deformation generator. The central result is the operator flow in Eq. (58), which identifies the Heisenberg evolution of the surface metric operator and reduced stress tensor with the T\bar{T} flow equations of Eq. (50).

Significance. If the claimed mapping were established, the paper would provide a dynamical mechanism for surface growth in terms of T\bar{T} deformation, connecting tensor-network bulk reconstruction to solvable irrelevant deformations of 2D CFTs. The paper contains useful building blocks: the generalized OSED tensor network of Sec. III.A removes the halving restriction of the original construction; the entropy monotonicity argument in Sec. III.B is plausible; and the BTZ radial-flow computation in Sec. III.C is a concrete consistency check. However, the central equivalence is not derived. The operators in Sec. IV.B are defined through their expectation values, and their evolution is then set equal to the T\bar{T} flow. As a result, the paper's headline claim currently rests on an ansatz rather than on a derivation from the tensor-network construction, so the significance of the result is not yet established.

major comments (4)
  1. [Sec. IV.B, Eq. (58)] The central evolution law (58) is posited rather than derived. The operators \gamma_{ab} and \hat{T}_{ab} are introduced in Eq. (52) only through their expectation values, and their unitary Heisenberg evolution is then set equal to the T\bar{T} flow of Eq. (50). The unitary U is characterized in Sec. III.D only by abstract composition and Hermiticity rules, and the generator A(x) is never expressed in terms of the layer-to-layer isometries W^{(k)} of the generalized OSED network. Consequently, the paper's main conclusion, that T\bar{T} deformation provides the dynamical mechanism for surface growth, is an input assumption rather than an output of the construction; the commutator algebra (59)-(64) is obtained by expanding (58) and therefore re-encodes the same assumption.
  2. [Sec. IV.B, Eqs. (53)-(55)] The surface-growth version of Zamolodchikov's factorization is assumed. Equation (53) is posed as a required condition, and Eq. (55) then imposes the factorization on Tr(\rho_V(0) \hat{T}_{ac} \gamma^{cd} \hat{T}_{db}). In a generic state \rho_V(0) this factorization does not hold; the paper does not show that \rho_V(0) is of the special form for which the CFT vacuum factorization (54) applies. This unsupported assumption is load-bearing for the derivation of the operator flow.
  3. [Sec. IV.B, Eqs. (62)-(64)] The decomposition A(x)=K(x)+Q and the interpretation of Q as a coarse-graining operator that reduces the dimension of labels are in tension with the unitary evolution (56)-(57). A unitary U cannot reduce Hilbert-space dimension, whereas the tensor-network layer transitions are implemented by isometric rather than unitary tensors W^{(k)}. The paper does not explain how a dimension-reducing coarse grainer generates a unitary flow, and the algebra (63)-(64) is derived by expanding the assumed flow (58), so it does not provide independent support for the construction.
  4. [Sec. III.C and Sec. IV.A, Eq. (51)] The identification of the radial parameter with the deformation parameter \mu is assumed rather than derived. The BTZ analysis (28)-(35) demonstrates geometric convergence of the grown surfaces to the horizon, but it does not fix the generator A(x) of U(\mu,0) nor the relation between the surface-growth step and the T\bar{T} flow parameter. Equation (51) imports identifications from the mixed-boundary-condition duality literature (g^{(0)}_{ab}=\gamma^{(0)}_{ab}, \rho_c = -\mu/C); these are not derived from the surface-growth dynamics, and without them the claimed mapping is not established.
minor comments (5)
  1. [Throughout] The manuscript contains several typographical errors, including 'the path-order does not effect the result' in Sec. IV.B and a duplicated reference: [15] is identical to [7].
  2. [Eqs. (60), (63), (64)] The index-position convention for the metric operator, e.g. \gamma_{ac}\gamma^{cb}=\delta_a^b and the products such as \gamma_{ac}\hat{T}^{cd}\gamma_{db}, is not defined consistently; please state whether indices are raised with the undeformed metric and clarify the ordering of operator products.
  3. [Sec. III.B] The text says that surfaces approach the horizon after finite steps, citing [18], but the proof in (21)-(26) establishes convergence only in the k\to\infty limit; please clarify which claim is being made.
  4. [Sec. III.C, Eq. (34)] The solution (34) of the differential equation (33) is a key check, but the integration steps are omitted; including them would help the reader verify the radial trajectory and the horizon limit (35).
  5. [Figs. 3 and 4] The figures are not described in enough detail in the text; a few sentences explaining what is plotted, and how the tensor labels correspond to boundary segments and radial layers, would improve readability.

Circularity Check

3 steps flagged · score 9.0 of 10

Central claim is built in: Eq. (52) defines surface-growth operators via T̄T-deformed expectation values, and Eq. (58) posits their Heisenberg evolution to be exactly the T̄T flow; the subsequent commutator derivation only unpacks this assumption.

  1. self definitional [Section IV.B, Eq. (52)]
    "Tr(ρV (0) ˆTab) = ˆT (0) ab , ... Tr(ρV (µ)γab) = γ(µ) ab = γ(0) ab − 2µ ˆT (0) ab + µ2 ˆT (0) ac γcd (0) ˆT (0) db , Tr(ρV (µ) ˆTab) = ˆT (µ) ab = ˆT (0) ab − µ ˆT (0) ac γcd (0) ˆT (0) db , where ˆT (µ) ab = ⟨ ˆTab⟩(µ) is the expectation value of ˆTab in T ¯T -deformed CFT2, and γ(µ) ab is the deformed metric, while Tr(ρV (µ)γab) and Tr(ρV (µ) ˆTab) are the expectation values defined by eq.(43) at the growing surfaces."

    The operators γab and ˆTab are not derived from the tensor network; they are defined by demanding that their expectation values at the growing surfaces equal the T̄T-deformed CFT metric and stress tensor, which already obey the T̄T flow (50). Therefore the later claim that surface growth reproduces T̄T deformation is contained in these definitions: the map is constructed as equality of expectation values, not predicted by the surface growth dynamics. The tensor network supplies only the state ρV(μ); it does not fix these operator identifications.

  2. fitted input called prediction [Section IV.B, Eq. (58)]
    "By moving to the ”Heisenberg picture”, the evolution of γab and ˆTab is given by U†(µ, 0)γabU(µ, 0) = γab − 2µ ˆTab + µ2 ˆTacγcd ˆTdb, U†(µ, 0) ˆTabU(µ, 0) = ˆTab − µ ˆTacγcd ˆTdb."

    This equation simply re-asserts the T̄T flow equations (50) as the evolution of the surface-growth operators. No derivation from the layer-to-layer isometries W˜(k) or from the continuum limit fixes U(μ,0) or its Hermitian generator A(x); in Sec. III.D, U was introduced only through abstract group properties (39). The commutator algebra (59)–(64), the decomposition A(x)=K(x)+Q, and the final claim i[Q,O] ∼ ∂μ⟨O⟩μ all follow by expanding (58), so they are unpackings of the assumed flow, not independent evidence. The central identification of radial surface growth with T̄T deformation is thus posited as a dynamical input.

1 more flagged steps
  1. self definitional [Section IV.B, Eqs. (53)–(55)]
    "Furthermore, this definition requires that Tr(ρV (0) ˆTacγcd ˆTdb) = ⟨ ˆTacγcd ˆTdb⟩(0). With Zamolodchikov’s factorization formula in CFT2 ⟨ ˆTacγcd ˆTdb⟩(0) = ⟨ ˆTac⟩(0)γcd(0)⟨ ˆTdb⟩(0), we can obtain the same formula in surface growth scheme Tr(ρV (0) ˆTacγcd ˆTdb) = Tr(ρV (0) ˆTac) Tr(ρV (0)γcd) Tr(ρV (0) ˆTdb)."

    The factorization property for surface-growth operators is not derived from the growth process; it is imposed by requiring equality with the CFT factorization formula. This forces the operator algebra of the surface growth scheme to match the T̄T/CFT structure, so the later derivation of the same operator algebra is a consequence of the requirement rather than a test of the surface-growth/T̄T correspondence.

full rationale

The central claim that T̄T deformation provides the dynamical mechanism for surface growth reduces, at the hinge of the paper (Sec. IV.B), to an identification made by hand. In Eq. (52), the bulk operators γab and ˆTab are defined only through expectation values, and their expectation values at the growing surfaces are set equal to the T̄T-deformed CFT metric and stress tensor, which already satisfy the flow (50). Then Eq. (58) posits that the unitary Heisenberg evolution of these operators is exactly the T̄T flow. The derivation of commutators (59)–(64), the split A=K+Q into disentangler and coarse-grainer, and the final equation i[Q,O] ∼ ∂μ⟨O⟩μ are algebraic expansions of this assumed relation; they do not independently establish that radial surface growth is T̄T flow. The tensor network of Sec. III fixes neither U nor A: U was introduced only with abstract group properties (39), and the identification of the radial parameter with the T̄T deformation parameter μ is made in (51) by comparison with the Fefferman-Graham expansion, not derived from the surface growth dynamics. The factorization condition (53)–(55) is likewise imposed from the CFT factorization formula. The BTZ and OSED computations are genuine geometric checks, but they do not ground the operator identification. Thus the paper's advertised result is an ansatz built into the definitions: the target relation is the input. This is internal circularity, not primarily a self-citation issue; citations to prior work by the same authors [17,18] supply the surface-growth geometry but not the T̄T identification. Score 9.

Assumptions & free parameters 0 free parameters · 8 assumptions · 2 invented entities

The central claim rests on two ad hoc postulates: the T\bar T flow equations (58) imposed on surface-growth operators and the factorization assumption (55). The geometric and tensor-network sections provide independent scaffolding, but the dynamical connection to T\bar T deformation is not derived from them.

assumptions (8)
  • domain assumption AdS3/CFT2 correspondence and the Ryu-Takayanagi formula hold.
    Used throughout to identify bulk minimal surfaces with boundary entanglement entropies; standard in the cited framework.
  • domain assumption The OSED tensor network faithfully represents the surface growth scheme.
    Inherited from [17,19]; this paper generalizes it but does not prove the representation.
  • domain assumption T\bar T deformation is dual to a finite radial cutoff or mixed boundary conditions in AdS3.
    Standard result cited from [42,43]; used in section IV.A to match the Fefferman-Graham expansion.
  • standard math The Fefferman-Graham expansion in 3D truncates at second order.
    Standard property used in eq. (47).
  • ad hoc to paper The surface-growth operators gamma_ab and T_hat_ab obey the T\bar T flow equations (58).
    Posited without derivation; this is the load-bearing assumption that makes the central claim true by construction.
  • ad hoc to paper Zamolodchikov factorization applies to the expectation value in the state rho_V(0).
    Eq. (55) uses the CFT vacuum factorization (54) for a general surface-growth density matrix; no proof is given.
  • ad hoc to paper The metric operator satisfies gamma_ac gamma^cb = delta_a^b.
    Used in appendix B to derive (60); consistency with the stress tensor is not checked.
  • domain assumption The growth entropy sequence S(k) is strictly decreasing and converges to S_h/N.
    Section III.B asserts S(k)<S(k-1) from isometric tensor dimension reduction and invokes monotone convergence; the identification of Hilbert-space dimension with entanglement entropy is heuristic.
invented entities (2)
  • Coarse-graining operator Q
    purpose: Generates the surface growth step; claimed to encode bulk diffeomorphism invariance (eq. 65).
    Q is defined by the commutators (63); no falsifiable handle or independent construction is provided.
  • Disentangler operator K
    purpose: Component of the generator A(x); commutes with gamma and T_hat.
    Introduced for the decomposition A=K+Q; carries no observable content in the paper.

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Pith. "Pith review of Surface growth scheme for bulk reconstruction and $T\bar T$ deformation." pith.science (2026). https://pith.science/paper/SXCN4FTS

@misc{pith2026250718435,
  author       = {Pith},
  title        = {Pith review of: Surface growth scheme for bulk reconstruction and $T\bar T$ deformation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SXCN4FTS}},
  note         = {Machine review of arXiv:2507.18435}
}
abstract

In this paper, we study the dynamical connection between the surface growth scheme and the conformal field theory with $T\bar{T}$ deformation. By utilizing the extended one-shot entanglement distillation tensor network, we find that the iterative growth, i.e. radial evolution of homogenous and isotropic bulk minimal surfaces in asymptotically anti-de Sitter (AdS) spacetime can be mapped to the $T\bar{T}$ operator flow driven by the deformation parameter. Our results show that the $T\bar{T}$ deformation can provide a dynamical mechanism for the surface growth in asymptotically AdS spacetime, which may shed light on reconstructing bulk gravitational dynamics from the surface growth scheme.

Figures

Figures reproduced from arXiv: 2507.18435 by the authors.

Figure 1
Figure 1. FIG. 1: The bulk minimal surface [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: The first layer (a) and the second layer (b) of original surface growth scheme with [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: The left is the tensor network of general surface growth scheme with [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: FIG. 4: The partition number [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5: Homogenous and isotropic surface growth from the cutoff surface [PITH_FULL_IMAGE:figures/full_fig_p012_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6: The connection between surface growth scheme and [PITH_FULL_IMAGE:figures/full_fig_p017_6.png]

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Cited by 2 Pith papers

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  1. Timelike Entanglement First Law and Linearized Field Equations in Higher Curvature Gravity

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  2. Entanglement first law for timelike entanglement entropy and linearized Einstein's equation

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Reference graph

Works this paper leans on

46 extracted references · 4 canonical work pages · cited by 2 Pith papers

  1. [1]

    The large N limit of superconformal field theories and supergravity,

    J. M. Maldacena, “The large N limit of superconformal field theories and supergravity,” Adv. Theor. Math. Phys. 2, 231 (1998) [Int. J. Theor. Phys. 38, 1113 (1999)] [arXiv:hep-th/9711200]

    arXiv 1998

  2. [2]

    Gauge theory correlators from non-critical string theory,

    S. S. Gubser, I. R. Klebanov and A. M. Polyakov, “Gauge theory correlators from non-critical string theory,” Phys. Lett. B 428, 105 (1998) [arXiv:hep-th/9802109]

    arXiv 1998

  3. [3]

    Anti-de Sitter space and holography,

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

    arXiv 1998

  4. [4]

    Holographic representation of local bulk operators,

    A. Hamilton, D. N. Kabat, G. Lifschytz and D. A. Lowe, “Holographic representation of local bulk operators,” Phys. Rev. D 74, 066009 (2006) [arXiv:hep-th/0606141 [hep-th]]

    arXiv 2006

  5. [5]

    The Gravity Dual of a Density Matrix,

    B. Czech, J. L. Karczmarek, F. Nogueira and M. Van Raamsdonk, “The Gravity Dual of a Density Matrix,” Class. Quant. Grav. 29, 155009 (2012) [arXiv:1204.1330 [hep-th]]. 21

    arXiv 2012

  6. [6]

    Causality & holographic entanglement entropy,

    M. Headrick, V. E. Hubeny, A. Lawrence and M. Rangamani, “Causality & holographic entanglement entropy,” JHEP 12, 162 (2014) [arXiv:1408.6300 [hep-th]]

    arXiv 2014

  7. [8]

    Entanglement Wedge Re- construction via Universal Recovery Channels,

    J. Cotler, P. Hayden, G. Penington, G. Salton, B. Swingle and M. Walter, “Entanglement Wedge Re- construction via Universal Recovery Channels,” Phys. Rev. X 9, no.3, 031011 (2019) [arXiv:1704.05839 [hep-th]]

    arXiv 2019

  8. [9]

    Bulk locality from modular flow,

    T. Faulkner and A. Lewkowycz, “Bulk locality from modular flow,” JHEP 07, 151 (2017) [arXiv:1704.05464 [hep-th]]

    arXiv 2017

Show all 46 references
  1. [10]

    TASI Lectures on the Emergence of Bulk Physics in AdS/CFT,

    D. Harlow, “TASI Lectures on the Emergence of Bulk Physics in AdS/CFT,” PoS T ASI2017, 002 (2018) [arXiv:1802.01040 [hep-th]]

    2018 arXiv

  2. [11]

    Towards Bulk Metric Reconstruction from Extremal Area Variations,

    N. Bao, C. Cao, S. Fischetti and C. Keeler, “Towards Bulk Metric Reconstruction from Extremal Area Variations,” Class. Quant. Grav. 36, no.18, 185002 (2019) [arXiv:1904.04834 [hep-th]]

    2019 arXiv

  3. [12]

    Holographic derivation of entanglement entropy from AdS/CFT,

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

    2006 arXiv

  4. [13]

    Aspects of Holographic Entanglement Entropy,

    S. Ryu and T. Takayanagi, “Aspects of Holographic Entanglement Entropy,” JHEP 0608, 045 (2006) [hep-th/0605073]

    2006 arXiv

  5. [14]

    A Covariant holographic entanglement entropy proposal,

    V. E. Hubeny, M. Rangamani and T. Takayanagi, “A Covariant holographic entanglement entropy proposal,” JHEP 0707, 062 (2007) [arXiv:0705.0016 [hep-th]]

    2007 arXiv

  6. [15]

    Reconstruction of Bulk Operators within the Entanglement Wedge in Gauge-Gravity Duality,

    X. Dong, D. Harlow, and A. C. Wall, “Reconstruction of Bulk Operators within the Entanglement Wedge in Gauge-Gravity Duality,” [hep-th/1601.05416]

    arXiv

  7. [17]

    Surface growth scheme for bulk reconstruction and tensor network,

    Y. Y. Lin, J. R. Sun and Y. Sun, “Surface growth scheme for bulk reconstruction and tensor network,” JHEP 12 (2020), 083 [arXiv:2010.01907 [hep-th]]

    2020 arXiv

  8. [18]

    Note on surface growth approach for bulk reconstruction,

    C. Yu, F. Z. Chen, Y. Y. Lin, J. R. Sun and Y. Sun, “Note on surface growth approach for bulk reconstruction,” Chin. Phys. C 46 (2022) no.8, 085104 [arXiv:2010.03167 [hep-th]]

    2022 arXiv

  9. [19]

    Beyond toy models: Distilling tensor networks in full AdS/CFT,

    N. Bao, G. Penington, J. Sorce, and A. C. Wall, “Beyond toy models: Distilling tensor networks in full AdS/CFT,” arXiv:1812.01171 [hep-th]

    arXiv

  10. [20]

    Entanglement renormalization,

    G. Vidal, “Entanglement renormalization,” Phys. Rev. Let. 99, 220405 (2007) [cond-mat/0512165]

    2007 arXiv

  11. [21]

    A class of quantum many-body states that can be efficiently simulated,

    G. Vidal, “A class of quantum many-body states that can be efficiently simulated,” Phys. Rev. Lett. 101, 110501 (2008) [quant-ph/0610099]

    2008 arXiv

  12. [22]

    Geometric interpretation of the multi-scale entanglement renormalization ansatz,

    A. Milsted and G. Vidal “Geometric interpretation of the multi-scale entanglement renormalization ansatz,” [hep-th/1812.00529]

    arXiv

  13. [23]

    Communication cost of entanglement transformations,

    P. Hayden and A. Winter, “Communication cost of entanglement transformations,” Phys. Rev. A 67 (2003)012326 [quant-ph/0204092]

    2003 arXiv

  14. [24]

    Bit thread, entanglement distillation, and entanglement of purifica- 22 tion,

    Y. Y. Lin, J. R. Sun and Y. Sun, “Bit thread, entanglement distillation, and entanglement of purifica- 22 tion,” Phys. Rev. D 103, no.12, 126002 (2021) [arXiv:2012.05737 [hep-th]]

    2021 arXiv

  15. [25]

    Surface growth approach for bulk reconstruction in the AdS/BCFT correspondence*,

    X. H. Fang, F. Z. Chen and J. R. Sun, “Surface growth approach for bulk reconstruction in the AdS/BCFT correspondence*,” Chin. Phys. C 48, no.6, 065106 (2024) [arXiv:2403.12086 [hep-th]]

    2024 arXiv

  16. [26]

    Expectation value of composite field T anti-T in two-dimensional quantum field theory,

    A. B. Zamolodchikov, “Expectation value of composite field T anti-T in two-dimensional quantum field theory,” [arXiv:hep-th/0401146 [hep-th]]

    arXiv

  17. [27]

    On space of integrable quantum field theories,

    F. A. Smirnov and A. B. Zamolodchikov, “On space of integrable quantum field theories,” Nucl. Phys. B 915 (2017), 363-383 doi:10.1016/j.nuclphysb.2016.12.014 [arXiv:1608.05499 [hep-th]]

    2017 arXiv

  18. [28]

    T ¯T -deformed 2D Quantum Field Theories,

    A. Cavagli` a, S. Negro, I. M. Sz´ ecs´ enyi and R. Tateo, “T ¯T -deformed 2D Quantum Field Theories,” JHEP 10 (2016), 112 doi:10.1007/JHEP10(2016)112 [arXiv:1608.05534 [hep-th]]

    2016 arXiv

  19. [29]

    T ¯T deformation of correlation functions,

    J. Cardy, “ T ¯T deformation of correlation functions,” JHEP 12 (2019), 160 doi:10.1007/JHEP12(2019)160 [arXiv:1907.03394 [hep-th]]

    2019 arXiv

  20. [30]

    Cutoff AdS 3 versus the TT deformation,

    P. Kraus, J. Liu and D. Marolf, “Cutoff AdS 3 versus the TT deformation,” JHEP 07 (2018), 027 doi:10.1007/JHEP07(2018)027 [arXiv:1801.02714 [hep-th]]

    2018 arXiv

  21. [31]

    Correlation functions, entanglement and chaos in the TT/JT -deformed CFTs,

    S. He and H. Shu, “Correlation functions, entanglement and chaos in the TT/JT -deformed CFTs,” JHEP 02 (2020), 088 doi:10.1007/JHEP02(2020)088 [arXiv:1907.12603 [hep-th]]

    2020 arXiv

  22. [32]

    The correlation function of (1,1) and (2,2) supersymmetric theories with T ¯T deformation,

    S. He, J. R. Sun and Y. Sun, “The correlation function of (1,1) and (2,2) supersymmetric theories with T ¯T deformation,” JHEP 04, 100 (2020) [arXiv:1912.11461 [hep-th]]

    2020 arXiv

  23. [33]

    Correlation functions of CFTs on a torus with a TT deformation,

    S. He and Y. Sun, “Correlation functions of CFTs on a torus with a TT deformation,” Phys. Rev. D 102 (2020) no.2, 026023 doi:10.1103/PhysRevD.102.026023 [arXiv:2004.07486 [hep-th]]

    2020 arXiv

  24. [34]

    Correlation functions in the TsT /TT correspondence,

    W. Cui, H. Shu, W. Song and J. Wang, “Correlation functions in the TsT /TT correspondence,” JHEP 04 (2024), 017 doi:10.1007/JHEP04(2024)017 [arXiv:2304.04684 [hep-th]]

    2024 arXiv

  25. [35]

    Entanglement entropy andTT deformation,

    W. Donnelly and V. Shyam, “Entanglement entropy andTT deformation,” Phys. Rev. Lett. 121 (2018) no.13, 131602 doi:10.1103/PhysRevLett.121.131602 [arXiv:1806.07444 [hep-th]]

    2018 arXiv

  26. [36]

    Entanglement entropy in TT -deformed CFT,

    B. Chen, L. Chen and P. X. Hao, “Entanglement entropy in TT -deformed CFT,” Phys. Rev. D 98 (2018) no.8, 086025 doi:10.1103/PhysRevD.98.086025 [arXiv:1807.08293 [hep-th]]

    2018 arXiv

  27. [37]

    Note on the R´ enyi entropy of 2D perturbed fermions,

    Y. Sun and J. R. Sun, “Note on the R´ enyi entropy of 2D perturbed fermions,” Phys. Rev. D 99, no.10, 106008 (2019) [arXiv:1901.08796 [hep-th]]

    2019 arXiv

  28. [38]

    W. X. Lai, H. Wang and Y. Xu, [arXiv:2507.15220 [hep-th]]

  29. [39]

    Geometric Formulation of General- ized Root-T ¯T Deformations,

    H. Babaei-Aghbolagh, S. He, T. Morone, H. Ouyang and R. Tateo, “Geometric Formulation of General- ized Root-T ¯T Deformations,” Phys. Rev. Lett. 133, no.11, 111602 (2024) [arXiv:2405.03465 [hep-th]]

    2024 arXiv

  30. [40]

    A pedagogical review on solvable irrelevant deformations of 2D quantum field theory,

    Y. Jiang, “A pedagogical review on solvable irrelevant deformations of 2D quantum field theory,” Commun. Theor. Phys. 73 (2021) no.5, 057201 doi:10.1088/1572-9494/abe4c9 [arXiv:1904.13376 [hep- th]]

    2021 arXiv

  31. [41]

    TT Deformation: Introduction and Some Recent Advances,

    S. He, Y. Li, H. Ouyang and Y. Sun, “ TT Deformation: Introduction and Some Recent Advances,” [arXiv:2503.09997 [hep-th]]

    arXiv

  32. [42]

    T ¯T and the mirage of a bulk cutoff,

    M. Guica and R. Monten, “ T ¯T and the mirage of a bulk cutoff,” SciPost Phys. 10 (2021) no.2, 024 doi:10.21468/SciPostPhys.10.2.024 [arXiv:1906.11251 [hep-th]]. 23

    2021 arXiv

  33. [43]

    Moving the CFT into the bulk with TT ,

    L. McGough, M. Mezei and H. Verlinde, “Moving the CFT into the bulk with TT ,” JHEP 04, 010 (2018) [arXiv:1611.03470 [hep-th]]

    2018 arXiv

  34. [44]

    Continuous Multiscale Entan- glement Renormalization Ansatz as Holographic Surface-State Correspondence,

    M. Miyaji, T. Numasawa, N. Shiba, T. Takayanagi and K. Watanabe, “Continuous Multiscale Entan- glement Renormalization Ansatz as Holographic Surface-State Correspondence,” Phys. Rev. Lett. 115, no.17, 171602 (2015) [arXiv:1506.01353 [hep-th]]

    2015 arXiv

  35. [45]

    Surface/State Correspondence as a Generalized Holography,

    M. Miyaji and T. Takayanagi, “Surface/State Correspondence as a Generalized Holography,” PTEP 2015, no.7, 073B03 (2015) [arXiv:1503.03542 [hep-th]]

    2015 arXiv

  36. [46]

    Surface/state correspondence and TT deformation,

    B. Chen, L. Chen and C. Y. Zhang, “Surface/state correspondence and TT deformation,” Phys. Rev. D 101, no.10, 106011 (2020) [arXiv:1907.12110 [hep-th]]

    2020 arXiv

  37. [47]

    The Holographic Weyl anomaly,

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

    1998

  38. [48]

    A Stress tensor for Anti-de Sitter gravity,

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

    1999 arXiv

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