An Infalling Observer and Behind the Horizon Cutoff

Amin Akhavan; Mohsen Alishahiha

REVIEW 3 major objections 5 minor 31 references

An Infalling Observer and Behind the Horizon Cutoff

T0 review · 3 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read The paper derives a fixed relation between a UV cutoff and a cutoff behind the horizon, matching holographic complexity.

desk verdict Clean but incremental: an alternative derivation of the authors' own behind-the-horizon cutoff result, with a genuinely unjustified step from scalar factorization to the graviton effective action. read the letter →

arxiv 1908.03502 v2 pith:W47IBHJD submitted 2019-08-08 hep-th

Amin Akhavan , Mohsen Alishahiha This is my paper · ORCID

classification hep-th

keywords blackholeinteriorPapadodimas-RajuoperatorspartitionfunctionUVcutoffbehindthehorizonholographiccomplexityeternalgeneralizedfreefields

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

Using the Papadodimas–Raju construction of interior operators, this paper establishes a general relation between partition functions for the inside and outside of an eternal black hole: the interior partition function is proportional to the product of the left- and right-exterior partition functions, and for identical exterior modes it is the square of either one. Treating the graviton effective action at leading order as the on-shell action, the authors convert this into a relation between cutoff versions of the actions and derive a formula that fixes a behind-the-horizon cutoff $r_0$ in terms of the UV cutoff $r_c$ and the horizon radius $r_h$. The formula, Eq. (24), is exactly the one previously obtained from holographic complexity. If correct, it means a physicist who imposes a finite UV cutoff—for example through a $T\bar{T}$-type deformation—cannot leave the interior of the black hole uncut; the interior cutoff is forced by the exterior one.

What carries the argument

The load-bearing object is the Papadodimas–Raju interior operator $\varphi^{(II)}_{\mathrm{CFT}}$, a CFT operator built from two copies of exterior generalized free fields, $O_{\omega,k}$ and $\tilde{O}_{\omega,k}$, with the same Klein–Gordon modes continued through the horizon. The key identity is large-$N$ factorization of correlators for generalized free fields, $$\langle O_1\cdots O_n \tilde{O}_1\cdots \tilde{O}_m\rangle = \langle O_1\cdots O_n\rangle \langle \tilde{O}_1\cdots \tilde{O}_m\rangle + O(1/N),$$ which yields $Z^{(II)} \propto Z^{(I)} Z^{(III)}$. The rest of the argument is a saddle-point computation: the Einstein–Hilbert action with Gibbons–Hawking and counterterm terms is evaluated on shell in regions I and II, with and without the radial cutoff, and the cutoff/no-cutoff difference is equated between the two regions through the exponentiated relation. This comparison produces Eq. (24), the fixed relation between $r_0$, $r_c$, and $r_h$.

What would settle it

Compute the one-loop (i.e., $O(1/N)$) graviton partition function in region II with the interior cutoff in place and check whether the exact relation $\Gamma^{(II)} = 2\Gamma^{(I)} + \text{const}$ survives; any non-vanishing $1/N$ correction would modify Eq. (24), and the deviation would show up as a shift in the effective cutoff $r_0$ inferred from interior correlators.

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Extended reading notes

Core claim

The central discovery is the factorization of interior physics: for generalized free fields with large-$N$ factorization, the interior partition function satisfies $Z^{(II)} \propto Z^{(I)} Z^{(III)}$, and for an eternal black hole with commuting left and right operators, $Z^{(II)} \propto (Z^{(I)})^2$. Promoting this proportionality to the graviton effective action through $e^{i\Gamma^{(II)}} \propto e^{2i\Gamma^{(I)}}$ and comparing on-shell actions with and without a cutoff at $r = r_c$, the paper derives $$\frac{1}{$r_0^{{d+1}}$}\left(\sqrt{\frac{$r_0^{{d+1}}$}{$r_h^{{d+1}}$} - 1} - 1\right) = \frac{1}{$r_c^{{d+1}}$}\left(1 - \sqrt{1 - \frac{$r_c^{{d+1}}$}{$r_h^{{d+1}}$}}\right)^2,$$ which fixes the behind-the-horizon cutoff $r_0$ once the exterior cutoff $r_c$ is chosen. In the small-cutoff limit this reduces to $r_0 r_c^2 \approx 2^{4/(d+1)} r_h^3$. The authors also show that unequal left/right cutoffs lead to a symmetric generalization, Eq. (26), and that a half-sided geometry (one exterior side capped) still induces an interior cutoff. The result matches the cutoff relation found earlier in holographic complexity, and the paper points out that the different powers of $r_0$ and $r_c$ in the small-cutoff limit are explained by the interior being built from two copies of exterior modes.

Load-bearing premise

The argument assumes without proof that the relation 'interior partition function equals the square of the exterior one,' derived for free scalar fields in the large-$N$ limit, also applies to the gravitational action itself; if the gravitational on-shell action does not factorize this way, Eq. (24) does not follow.

Editorial extensions

If this is right

A finite UV cutoff at $r_c$ forces a behind-the-horizon cutoff $r_0$ given by Eq. (24); the interior cutoff is not an independent choice.
For small cutoffs, $r_0 r_c^2 \approx 2^{4/(d+1)} r_h^3$, so moving the boundary cutoff inward pushes the interior cutoff toward the horizon with a different power.
The same interior/exterior factorization predicts how unequal left and right cutoffs determine the interior cutoff, Eq. (26), which complexity computations did not directly address.
The result explains the power mismatch between $r_0$ and $r_c$ in the complexity literature as a consequence of the interior operator being formed from two copies of exterior modes.
If the proportionality $e^{i\Gamma^{(II)}} \propto e^{2i\Gamma^{(I)}}$ survives higher orders, the interior cutoff should be visible in other interior-sensitive quantities, such as commutators or entanglement probes.

Reading between the lines

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

One can test the relation beyond the saddle point: loop corrections to the on-shell actions should shift Eq. (24) by powers of $G_N$ (i.e., $1/N$), and measuring that shift would reveal how state-dependent the interior cutoff is.
The same factorization logic suggests a universal principle: any bulk or boundary cutoff that restricts exterior modes will restrict interior modes through the doubling of degrees of freedom, so interior reconstructions in any approach (not just the Papadodimas–Raju one) should exhibit an inherited cutoff.
For the typical-microstate geometry discussed in the paper, the predicted interior cutoff is larger by a factor $2^{2/(d+1)}$ when one exterior side is capped; this could serve as a sharp signature distinguishing a typical microstate from the full eternal black hole.
If $T\bar{T}$-like deformations are the physical origin of the UV cutoff, then the behind-the-horizon cutoff provides a concrete geometric target: finite-cutoff gravity should exhibit a modified interior geometry with a new boundary at $r_0$, and correlation functions of interior operators should reflect this boundary.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Short version: the paper is a competent re-derivation of a result the authors already published in [8], plus a few new asymmetric cutoff formulas. The on-shell action algebra is standard, and the final relation (24) follows from Eq. (14) without any obvious error. The main soft spot is that Eq. (14) is not actually derived for gravity.

The paper starts with the Papadodimas-Raju construction. For a generalized free scalar, large-N factorization gives Z^II proportional to Z^I Z^III, hence Z^II proportional to (Z^I)^2. That step is fine. The trouble appears right after Eq. (13): the same proportionality is extended to the graviton effective action, with only the remark that the leading effective action is the classical action. The stress tensor is not a generalized free field. It has a nonzero connected three-point function at leading order in the 1/N expansion, so the factorization in Eq. (10) does not apply. A nonlinear bulk extension of the interior-operator construction would be needed, and none is provided. Since Eq. (14) is the load-bearing relation, the main claim is conditional on an unproven assumption.

Second, the behind-the-horizon cutoff r0 is assumed to exist, not derived. The sentence "we will assume that there is also a finite radial cutoff behind the horizon" appears just before Eq. (23), and the word "enforce" in the abstract is too strong. What is actually shown is: if Eq. (14) holds for gravity and if such a cutoff exists, then consistency fixes its value. Those are real conditionals, but they are not enforcement.

Credit where it is due: the asymmetric formulas (26) and (29) are not in [8], and the relation Z^II proportional to Z^I Z^III gives a clean explanation of the power mismatch between r0 and rc. The paper is short, readable, and the action computations are transparent. The agreement with [8] is not suspicious—the overlap is stated—but it does mean the benchmark is self-referential, so it cannot validate the new derivation.

Who should read this: people working on holographic complexity and interior probes. It is a useful cross-check, not a breakthrough. I would send it to a serious referee rather than desk-reject, because the gap is identifiable and might be fixable by either a proper justification of the graviton step or by presenting Eq. (14) as a conjecture. As it stands, I would not cite it as the primary derivation of the behind-the-horizon cutoff.

Referee Report

3 major / 5 minor

Summary. The paper uses the Papadodimas-Raju construction of black-hole interior operators to propose a relation between the partition function of interior modes and the partition functions of the left and right exterior modes of an eternal black brane. For generalized free fields at large N the relation is Z^(II) ∝ Z^(I) Z^(III), which in the symmetric case becomes Z^(II) ∝ (Z^(I))^2. The paper then extends this relation to the graviton effective action, replaces the restricted partition functions by on-shell Einstein-Hilbert actions with Gibbons-Hawking and counterterm terms, and computes the effect of a finite radial UV cutoff r_c. By postulating a behind-the-horizon cutoff r_0, it derives Eq. (24), which fixes r_0 in terms of r_c and reproduces the cutoff relation obtained earlier in the holographic-complexity context. Generalizations to unequal left/right cutoffs and to a single exterior plus mirror-partner construction are given in Eqs. (26)-(29). The central new step is the application of the scalar factorization relation to gravity, and the central assumption is the existence of the behind-the-horizon cutoff r_0.

Significance. If the derivation were completed, Eq. (24) would be a concrete and checkable relation tying a UV cutoff to a cutoff behind the horizon, and it would explain the different powers of r_0 and r_c seen in the complexity analysis. The on-shell action computations are explicit, the small-cutoff asymptotics are clean, and the paper is honest about some of its own limitations: it assumes rather than derives the existence of r_0 before Eq. (23), and it acknowledges the heuristic nature of the restricted partition functions. The main strength is that the final relation is not a vague expectation but a specific equation that can be compared with independent computations. Its significance is currently conditional, because the derivation relies on an unproven scalar-to-graviton extension and on the existence of solutions to Eq. (24). The agreement with [8] is a useful consistency check, but it is not an independent external validation because [8] shares two of the present authors.

major comments (3)

[Section 3, after Eq. (13)] The extension of the factorization relation from the scalar case to the graviton effective action is not justified. Equation (10) relies on generalized free-field factorization at large N, a property that fails for the stress-tensor multiplet: the connected three-point function of the stress tensor is non-vanishing at leading order in 1/N and does not factorize. Since Eq. (14) and hence Eq. (24) are obtained by applying Eq. (13) to the Einstein-Hilbert action, the central result is unsupported at this step. The authors should either prove the graviton factorization at the required order or explicitly restrict the claim to scalar fields.
[Section 3, before Eq. (23)] The existence of the behind-the-horizon cutoff r_0 is assumed, not derived. The text states 'we will assume that there is also a finite radial cutoff behind the horizon located at r_0', but the abstract and conclusions claim that a UV cutoff 'enforces' a cutoff behind the horizon. At most, the computation shows that if r_0 exists, Eq. (24) fixes its value. Moreover, no existence proof is given: for r_c close to r_h the right-hand side of Eq. (24) approaches r_h^{-(d+1)}, while the left-hand side as a function of r_0>r_h is bounded above by approximately 0.207 r_h^{-(d+1)}; hence Eq. (24) has no real solution in that regime. The claimed enforcement should be restricted to a proven range of r_c.
[Section 3, Eqs. (7)-(9)] The 'restricted partition functions' Z^(I) and Z^(II) are not defined with sufficient precision. A bulk gravitational path integral is a global object; restricting it to field configurations of the form (3)-(5) is a formal manipulation, and the delta-functional remark in footnote 2 does not specify integration measures, boundary conditions on the cutoff surfaces, or the treatment of the horizon. The subsequent saddle-point identification of these objects with on-shell actions in separated bulk regions is therefore heuristic. The paper should either define these restricted partition functions carefully or present the on-shell-action relation as a conjecture motivated by the Papadodimas-Raju construction.

minor comments (5)

[Throughout] There are several typographical errors: 'Penrose digram' in Section 2 should be 'Penrose diagram'; 'redial' in Section 3 should be 'radial'; 'react into' before Eq. (22) should be 'recast into'; 'grater' in Section 4 should be 'greater'; 'gravity daul' in footnote 2 should be 'gravity dual'; and 'liner' in Section 3 should be 'linear'.
[Figure 1] Region IV is labeled in the Penrose diagram but is never defined or used in the text; please add a definition or remove the label.
[Eq. (24)] The domain of r_0 should be stated explicitly: the square root requires r_0>r_h, so the text should specify that the behind-the-horizon cutoff lies in the branch r_0>r_h rather than relying on the phrase 'behind the horizon' alone.
[Eqs. (11)-(14)] The proportionality constants in Eqs. (11) and (12) are not tracked; footnote 5 states that they are cutoff-independent, but this cutoff-independence is asserted rather than demonstrated. Please either prove it or state it as an additional assumption.
[Abstract] The phrase 'in terms those partition functions' is missing a word and should read 'in terms of those partition functions'.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular step: Eq. (24) is a derived consequence of the stated PR operator construction, large-N factorization, and the explicitly assumed interior cutoff; the agreement with [8] is a non-load-bearing self-citation.

full rationale

The paper's central partition-function relation, Z^II ∝ (Z^I)^2, is not presented as an independent empirical prediction. It is stated as a direct consequence of the Papadodimas-Raju interior-operator construction, Eq. (5), together with large-N factorization, Eq. (10). Eq. (14), which is then used to compare cutoffs, follows algebraically from Eq. (12)/(13). The on-shell actions in region I and region II are computed directly from the Einstein-Hilbert action with standard boundary terms, Eqs. (17)-(23). The behind-horizon cutoff r0 is explicitly introduced as an assumption ('we will assume that there is also a finite radial cutoff behind the horizon located at r0'), and Eq. (24) fixes its value by solving Eq. (14); this is a well-posed determination of an assumed parameter, not a fitted parameter renamed as a prediction. The agreement with [8] is a self-citation by overlapping authors, but no step of the derivation uses [8] as a premise; it is cited only as confirmation, so the self-citation is not load-bearing. The main validity risks, namely the unproven extension of the scalar factorization to the graviton effective action and the unproven existence of r0, are flagged in the text and are better classified as unsupported assumptions or correctness risks rather than circular reductions. Consequently, no circularity is found.

Assumptions & free parameters 1 free parameters · 5 assumptions · 1 invented entities

The central derivation rests on the assumed existence of a behind-the-horizon cutoff r0, the large N factorization of correlators, the saddle point approximation, and the unproven extension of a scalar factorization relation to the graviton. The only independent benchmark cited for the final cutoff relation is the authors' own prior work [8].

free parameters (1)

Behind-the-horizon cutoff r0 = Fixed by Eq. (24) in terms of UV cutoff rc
Its existence is introduced as an assumption to satisfy the consistency relation (14); the paper does not derive why a cutoff must exist.

assumptions (5)

domain assumption Large N factorization of correlators in the generalized free field limit (Eq. (10))
Used to factorize the partition function Z^(II) into Z^(I) Z^(III). Standard in AdS/CFT but a limit assumption.
domain assumption Saddle point approximation: the effective action equals the classical on-shell action at leading order
Needed to replace partition function relations with on-shell action relations (Eq. (13) to Eq. (14)).
ad hoc to paper The factorization relation derived for a scalar field applies also to the graviton effective action
Asserted without derivation after Eq. (13); this is the main conceptual leap.
domain assumption The proportionality constant in Eq. (14) is cutoff-independent
Stated in footnote 5 without detailed proof; needed to drop the constant when comparing cutoff and non-cutoff cases.
domain assumption Validity of the Papadodimas Raju interior operator construction
The whole relation Z^(II) ∝ Z^(I) Z^(III) rests on this construction; the paper acknowledges concerns about state dependence (refs [15-17]).

invented entities (1)

Behind-the-horizon cutoff surface at r = r0 independent evidence
purpose: Truncates the black hole interior near the singularity so that the on-shell action satisfies the factorization relation (14).
The paper predicts a definite relation (24) between r0 and the UV cutoff rc, and notes agreement with the holographic complexity result [8]. This provides a falsifiable handle, though the supporting computation is by the same authors.

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Cite this review

Pith. "Pith review of An Infalling Observer and Behind the Horizon Cutoff." pith.science (2026). https://pith.science/paper/W47IBHJD

@misc{pith2026190803502,
  author       = {Pith},
  title        = {Pith review of: An Infalling Observer and Behind the Horizon Cutoff},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/W47IBHJD}},
  note         = {Machine review of arXiv:1908.03502}
}

read the original abstract

Using Papadodimas and Raju construction of operators describing the interior of a black hole, we present a general relation between partition functions of operators describing inside and outside the black hole horizon. In particular for an eternal black hole the partition function of the interior modes may be given in terms those partition functions associated with the modes of left and right exteriors. By making use of this relation we observe that setting a finite UV cutoff will enforce us to have a cutoff behind the horizon whose value is fixed by the UV cutoff. The resultant cutoff is in agreement with what obtained in the context of holographic complexity.

Figures

Figures reproduced from arXiv: 1908.03502 by the authors.

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Works this paper leans on

31 extracted references · 4 canonical work pages

[8]

Complexity and Behind the Horizon Cut Oﬀ,

A. Akhavan, M. Alishahiha, A. Naseh and H. Zolﬁ, “Complexity and Behind the Horizon Cut Oﬀ,” JHEP 1812, 090 (2018) [arXiv:1810.12015 [hep-th]]

arXiv 2018
[1]

The Large N limit of superconformal ﬁeld theories and supergravity,

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

arXiv 1999
[2]

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]

arXiv 2006
[3]

Computational Complexity and Black Hole Horizons,

L. Susskind, “Computational Complexity and Black Hole Horizons,” arXiv:1403.5695 [hep-th], arXiv:1402.5674 [hep-th]

arXiv
[4]

Complexity and Shock Wave Geometries,

D. Stanford and L. Susskind, “Complexity and Shock Wave Geometries,” Phys. Rev. D 90, no. 12, 126007 (2014) [arXiv:1406.2678 [hep-th]]

arXiv 2014
[5]

Holographic Complexity Equals Bulk Action?,

A. R. Brown, D. A. Roberts, L. Susskind, B. Swingle and Y. Zhao, “Holographic Complexity Equals Bulk Action?,” Phys. Rev. Lett. 116, no. 19, 191301 (2016) [arXiv:1509.07876 [hep-th]]

arXiv 2016
[6]

Complexity, action, and black holes,

A. R. Brown, D. A. Roberts, L. Susskind, B. Swingle and Y. Zhao, “Complexity, action, and black holes,” Phys. Rev. D 93, no. 8, 086006 (2016) [arXiv:1512.04993 [hep-th]]. 9 SciPost Physics REFERENCES

arXiv 2016
[7]

Black hole subregion action and complexity,

M. Alishahiha, K. Babaei Velni and M. R. Mohammadi Mozaﬀar, “Black hole subregion action and complexity,” Phys. Rev. D 99, no. 12, 126016 (2019) [arXiv:1809.06031 [hep- th]]

arXiv 2019

Show all 31 references

[9]

On complexity of Jackiw-Teitelboim gravity,

M. Alishahiha, “On complexity of Jackiw-Teitelboim gravity,” Eur. Phys. J. C 79, no. 4, 365 (2019) [arXiv:1811.09028 [hep-th]]

2019 arXiv
[10]

Complexity and Near Extremal Charged Black Branes,

M. Alishahiha, K. Babaei Velni and M. R. Tanhayi, “Complexity and Near Extremal Charged Black Branes,” arXiv:1901.00689 [hep-th]

1901 arXiv
[11]

More on Complexity in Finite Cut Oﬀ Geometry,

S. S. Hashemi, G. Jafari, A. Naseh and H. Zolﬁ, “More on Complexity in Finite Cut Oﬀ Geometry,” arXiv:1902.03554 [hep-th]

1902 arXiv
[12]

Complexity of Hyperscaling Violating Theories at Finite Cutoﬀ,

M. Alishahiha and A. Faraji Astaneh, “Complexity of Hyperscaling Violating Theories at Finite Cutoﬀ,” arXiv:1905.10740 [hep-th]

1905 arXiv
[13]

An Infalling Observer in AdS/CFT,

K. Papadodimas and S. Raju, “An Infalling Observer in AdS/CFT,” JHEP 1310, 212 (2013) [arXiv:1211.6767 [hep-th]]

2013 arXiv
[14]

Behind the Horizon in AdS/CFT,

E. Verlinde and H. Verlinde, “Behind the Horizon in AdS/CFT,” arXiv:1311.1137 [hep- th]

arXiv
[15]

Violations of the Equivalence Principle by a Nonlocally Reconstructed Vacuum at the Black Hole Horizon,

R. Bousso, “Violations of the Equivalence Principle by a Nonlocally Reconstructed Vacuum at the Black Hole Horizon,” Phys. Rev. Lett. 112, no. 4, 041102 (2014) [arXiv:1308.3697 [hep-th]]

2014 arXiv
[16]

Gauge/Gravity Duality and the Black Hole Interior,

D. Marolf and J. Polchinski, “Gauge/Gravity Duality and the Black Hole Interior,” Phys. Rev. Lett. 111, 171301 (2013) [arXiv:1307.4706 [hep-th]]

2013 arXiv
[17]

Aspects of the Papadodimas-Raju Proposal for the Black Hole Interior,

D. Harlow, “Aspects of the Papadodimas-Raju Proposal for the Black Hole Interior,” JHEP 1411, 055 (2014) [arXiv:1405.1995 [hep-th]]

2014 arXiv
[18]

Emergent Spacetime and Holographic CFTs,

S. El-Showk and K. Papadodimas, “Emergent Spacetime and Holographic CFTs,” JHEP 1210, 106 (2012) [arXiv:1101.4163 [hep-th]]

2012 arXiv
[19]

Eternal black holes in anti-de Sitter,

J. M. Maldacena, “Eternal black holes in anti-de Sitter,” JHEP 0304, 021 (2003) [hep- th/0106112]

2003
[20]

An Introduction to quantum ﬁeld theory,

M. E. Peskin and D. V. Schroeder, “An Introduction to quantum ﬁeld theory,”
[21]

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,” hep-th/0401146

arXiv
[22]

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, 363 (2017) doi:10.1016/j.nuclphysb.2016.12.014 [arXiv:1608.05499 [hep-th]]

2017 arXiv
[23]

T ¯T -deformed 2D Quantum Field Theories,

A. Cavaglia, S. Negro, I. M. Szecsenyi and R. Tateo, “ T ¯T -deformed 2D Quantum Field Theories,” JHEP 1610, 112 (2016) doi:10.1007/JHEP10(2016)112 [arXiv:1608.05534 [hep-th]]. 10 SciPost Physics REFERENCES

2016 arXiv
[24]

Moving the CFT into the bulk with TT ,

L. McGough, M. Mezei and H. Verlinde, “Moving the CFT into the bulk with TT ,” JHEP 1804, 010 (2018) doi:10.1007/JHEP04(2018)010 [arXiv:1611.03470 [hep-th]]

2018 arXiv
[25]

TT deformations in general dimensions,

M. Taylor, “TT deformations in general dimensions,” arXiv:1805.10287 [hep-th]

arXiv
[26]

Holography at ﬁnite cutoﬀ with a T 2 deformation,

T. Hartman, J. Kruthoﬀ, E. Shaghoulian and A. Tajdini, “Holography at ﬁnite cutoﬀ with a T 2 deformation,” arXiv:1807.11401 [hep-th]

arXiv
[27]

A Note On Boundary Conditions In Euclidean Gravity,

E. Witten, “A Note On Boundary Conditions In Euclidean Gravity,” arXiv:1805.11559 [hep-th]

arXiv
[28]

T ¯T and the mirage of a bulk cutoﬀ,

M. Guica and R. Monten, “ T ¯T and the mirage of a bulk cutoﬀ,” arXiv:1906.11251 [hep- th]

1906 arXiv
[29]

Sphere partition functions and cut-oﬀ AdS,

P. Caputa, S. Datta and V. Shyam, “Sphere partition functions and cut-oﬀ AdS,” JHEP 1905, 112 (2019) [arXiv:1902.10893 [hep-th]]

2019 arXiv
[30]

Cutoﬀ Function in Holographic RG Flow,

F. Ardalan, “Cutoﬀ Function in Holographic RG Flow,” Phys. Rev. D 99, no. 10, 106016 (2019) [arXiv:1902.09123 [hep-th]]

2019 arXiv
[31]

On the interior geometry of a typical black hole microstate,

J. de Boer, R. Van Breukelen, S. F. Lokhande, K. Papadodimas and E. Verlinde, “On the interior geometry of a typical black hole microstate,” JHEP 1905 (2019) 010 [arXiv:1804.10580 [hep-th]]. 11

2019 arXiv

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [8]

Complexity and Behind the Horizon Cut Oﬀ,

A. Akhavan, M. Alishahiha, A. Naseh and H. Zolﬁ, “Complexity and Behind the Horizon Cut Oﬀ,” JHEP 1812, 090 (2018) [arXiv:1810.12015 [hep-th]]

arXiv 2018

[2] [1]

The Large N limit of superconformal ﬁeld theories and supergravity,

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

arXiv 1999

[3] [2]

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]

arXiv 2006

[4] [3]

Computational Complexity and Black Hole Horizons,

L. Susskind, “Computational Complexity and Black Hole Horizons,” arXiv:1403.5695 [hep-th], arXiv:1402.5674 [hep-th]

arXiv

[5] [4]

Complexity and Shock Wave Geometries,

D. Stanford and L. Susskind, “Complexity and Shock Wave Geometries,” Phys. Rev. D 90, no. 12, 126007 (2014) [arXiv:1406.2678 [hep-th]]

arXiv 2014

[6] [5]

Holographic Complexity Equals Bulk Action?,

A. R. Brown, D. A. Roberts, L. Susskind, B. Swingle and Y. Zhao, “Holographic Complexity Equals Bulk Action?,” Phys. Rev. Lett. 116, no. 19, 191301 (2016) [arXiv:1509.07876 [hep-th]]

arXiv 2016

[7] [6]

Complexity, action, and black holes,

A. R. Brown, D. A. Roberts, L. Susskind, B. Swingle and Y. Zhao, “Complexity, action, and black holes,” Phys. Rev. D 93, no. 8, 086006 (2016) [arXiv:1512.04993 [hep-th]]. 9 SciPost Physics REFERENCES

arXiv 2016

[8] [7]

Black hole subregion action and complexity,

M. Alishahiha, K. Babaei Velni and M. R. Mohammadi Mozaﬀar, “Black hole subregion action and complexity,” Phys. Rev. D 99, no. 12, 126016 (2019) [arXiv:1809.06031 [hep- th]]

arXiv 2019