Conformal Blocks Beyond the Semi-Classical Limit

A. Liam Fitzpatrick; Jared Kaplan

REVIEW

Conformal Blocks Beyond the Semi-Classical Limit

A. Liam Fitzpatrick, Jared Kaplan

High Energy Physics - Theory · Submitted 9 Dec 2015 · 30 references

Pith's verdict: A solid, honest next step in the heavy-light Virasoro program: the O(h_L/c) correction is genuinely new, and the interpretive section is flagged as conjecture rather than sold as a result.

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arXiv ID1512.03052 (version 3)

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CitationA. Liam Fitzpatrick, Jared Kaplan. "Conformal Blocks Beyond the Semi-Classical Limit." arXiv:1512.03052 (2015). https://pith.science/paper/ETC6W7OI

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Editor's note

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Short version: the new content here is real. This is the first explicit O(h_L/c) correction to the heavy-light Virasoro vacuum block, and that term is not visible in (1/c) log V at fixed h_L/c, so it genuinely sits outside the semiclassical limit rather than being a reshuffling of it. The O(h_L^2/c) piece overlaps with Beccaria–Fachechi–Macorini [17], and the paper says so plainly in the introduction. That disclosure is the right call and it is done without fuss. The closed forms in (1.4) and the general-block integral formulas in Appendix A are the kind of thing people will actually use, and the derivation — projector in w-coordinates, contour integrals reduced to (2.20), then evaluated — is a real first-principles computation, not a fit to anything. The small-z check against the Zamolodchikov recursion to O(z^8) is a genuine independent benchmark, and the authors are careful to say the monodromy story in Section 3 is a conjecture about image-summed propagators, not a derivation. I'd take that at face value; it's labeled honestly and shouldn't be read as a claim about resolving the information paradox, which they explicitly disclaim (abstract:s6 is an expectation, not a result). On the reader's main worry: I'd downgrade it. The mode-truncation counting in §2.1 is conservative, because the connected heavy-light T^{2k} correlator in w-coordinates scales as c, not c^k, so 4-L and higher terms are suppressed by extra powers of 1/c and can't contaminate O(1/c). The sharper gap is verification coverage. The O(z^8) comparison is done only at alpha → 1 (eq. 2.22), and the agreement with [17] is at the level of the integral (2.20), not the closed form. An algebra slip in the incomplete-Beta/harmonic-number evaluation at generic alpha would survive both checks. That's a bounded gap, not a refutation, but it's the one thing I'd ask for: a numerical evaluation of (1.4) at, say, alpha = 1.7i against a direct series. Footnote 3's branch-cut prescription is also a practical annoyance for anyone reusing the formula. Who should read it: people working on Virasoro blocks, AdS3 gravity, and thermalization in 2d CFT. I'd cite it. Send it to referees.

Referee report

Major objections (2)

[§2.1] The truncation to single and double L-modes at O(1/c) rests on the counting argument in §2.1: a correlator with 2k insertions of T can have at most c^k from TT contractions, against a norm suppression c^{-2k}, so the 2k-L term is at most c^{-k}. This is a bound, not a demonstration that the bound is saturated only by the modes retained, and it is load-bearing for the completeness of Eq. (1.4). The paper should state explicitly that this is a conservative bound and, ideally, supply a short argument or a check that triple- and higher-L contributions are genuinely absent at O(1/c) at generic alpha, not merely suppressed by the same counting. The O(z^8) check in §2.3 supports the truncation but only in the alpha -> 1 limit, so it does not by itself close this point.
[§2.3, Eq. (2.22); Eq. (1.4)] The independent verification is confined to the small-h_H limit: the O(z^8) comparison against ref. [18] is performed for the alpha -> 1 expressions in Eq. (2.22), and the comparison with ref. [17] is at the level of the integral representation of the semi-classical piece, not the closed form. The general-alpha closed form in Eq. (1.4) is therefore obtained by direct evaluation of the checked integrals (2.20) but is not itself independently expanded and matched at generic alpha. An algebra slip in the incomplete-Beta/harmonic-number evaluation at general alpha would survive the small-h_H check. A numerical comparison of Eq. (1.4) against the integral (2.20), or against the independent method of ref. [17], at one or two generic values (e.g. alpha = 0.7 and alpha = 1.3 i) would substantially strengthen confidence in the headline result and is the sharpest residual gap in the paper.

Minor objections (6)

[Abstract [s4]; Eq. (1.4); §2.2] The abstract states the corrections as 'semi-classical' h_L^2/c^2 and 'quantum' h_L/c^2, whereas Eq. (1.4) and the surrounding discussion in §2.2 give the corrections as O(h_L^2/c) and O(h_L/c). The body is the correct scaling (the projector factors in Eq. 2.13 supply 1/c^2, the light-operator overlaps supply h_L^2 or h_L, and the heavy T T correlator supplies one factor of c). The abstract should be corrected so that the headline statement matches the body.
[Eq. (1.4)] Several factors in Eq. (1.4) are typographically ambiguous as displayed, for example 'csch2(alpha t/2)2' and '12 log(2 sinh(alpha t/2) alpha )'. Since this equation is the central deliverable, it should be typeset so that the argument of each special function and the placement of each denominator are unambiguous.
[Eqs. (2.22), (2.26)] The overall 1/c bookkeeping and the sign of the leading z^4 coefficient should be stated explicitly when passing from Eq. (2.22) to the small-w series in Eq. (2.26). As printed, Eq. (2.22) carries no explicit 1/c while Eq. (2.26) does, and the leading coefficients appear to differ in sign; a reader cannot tell whether this reflects a convention for V^(1) or an inconsistency. A one-line statement of the convention would resolve it.
[Appendix A, Eq. (A.7); Abstract [s4]] The abstract promises 'integral formulas for general Virasoro blocks', but Appendix A leaves the functions G1 and G2 in Eq. (A.7) implicit ('we do not present them here'). Either the explicit G1, G2 should be written out, or the abstract should be softened to say that the general-block formula is given up to the constituent sums displayed in Eq. (A.6).
[§2.4; §2.2] The symbol T is used both for the stress tensor T(w) throughout §2 and for the temperature in the 'Large T limit' of §2.4. The two uses are close enough in the text to be confusing; a distinct symbol for temperature (or an explicit note at the start of §2.4) would help.
[§1.1; §2.4; footnote 5] In §1.1 the paper states the expectation that 'perturbative 1/c corrections should not violate the thermal periodicity', and §2.4 then finds that the 1/c corrections to the block do violate it. The reconciliation (the expectation applies to the full correlator, while the block's monodromy cancels against other blocks) is present but appears only later; it would be clearer to flag it at the point where the expectation is first stated. Separately, footnote 5 asserts that the monodromy under Tt -> Tt + 1 can be checked 'straightforwardly' from Eq. (2.24); showing the monodromy of the Ei/li terms explicitly would make that check verifiable by the reader.

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The paper

The paper claims

The first $1/c$ correction to the heavy-light Virasoro vacuum block is computed in closed form, and it breaks the thermal periodicity that the leading-order result obeys.

The reading

In two-dimensional conformal field theory, the Virasoro vacuum block in a background with one heavy operator and one light operator reproduces, at infinite central charge $c$, exactly the two-point function of a thermal state. That match is the sharpest CFT-side statement of black hole thermodynamics, and its failure at finite $c$ is a sharpest-form version of the information paradox: the thermal answer is periodic in Euclidean time, while a genuine four-point function in a finite-$c$ CFT cannot be. This paper pushes the computation one step further, extracting the terms of order $h_L/c$ and $h_L^2/c$ in the heavy-light expansion of the vacuum block and writing them in closed form. The corrections turn out not to be periodic in Euclidean time, and the authors argue this is not a contradiction: an individual conformal block is allowed unphysical monodromies that cancel once blocks are summed into a full correlator, and they sketch how the same monodromies arise from a bulk AdS$_3$ computation using geodesic Witten diagrams.

What carries the argument

The engine is a change of coordinates. Instead of the flat Virasoro generators $L_n$, the authors build the projector onto the exchanged representation out of modes defined in the coordinate $w = 1-(1-z)^{1/2}$, where the exponent is fixed by the heavy operator dimension through $1-24h_H/c$; in this basis the overlap with the heavy operator no longer grows with $h_H$, so the leading contribution comes only from the raising modes $L_{-n}$. The stress-tensor two-point function in the $w$ coordinate then acts as a generating function for the heavy-operator overlaps, and the norm matrix of the double modes is inverted and expanded to order $1/c^2$. A contour integral over two $w$-plane insertions of $T$ converts the projector sum into the closed-form correction functions, with the contour shrunk onto the branch cut between $0$ and $w$.

Extended reading notes

Core claim

The paper's central result is equation (1.4): the heavy-light Virasoro vacuum block, expanded to first order in $1/c$ at large temperature, is the leading semi-classical answer multiplied by a bracket $1 + (h_L/c)V^{(1)}_{h_L} + (h_L^2/c)V^{(1)}_{h_L^2}$, where both correction functions are given explicitly in terms of incomplete Beta functions, harmonic numbers, and elementary functions of the rescaled time and of $h_H/c$. The $h_L^2/c$ piece is semi-classical: it survives in the limit where $c$ is taken large with $h_H/c$ and $h_L/c$ held fixed, so it corresponds to classical gravitational backreaction of the light probe on the geometry. The $h_L/c$ piece is quantum: it drops out of $c^{-1}$ times the logarithm of the block in that same limit, so it is a genuine loop effect in the dual AdS$_3$ description rather than a correction to a classical saddle. The authors also give integral formulas, built from a contour representation of the Virasoro projector, that produce general heavy-light blocks order by order in $1/c$. Examining the corrections as functions of Euclidean time, they find logarithms of $1-w$ with $1-w = e^{2 i T t}$, hence a non-trivial monodromy under $t_E$ shifted by one thermal period: the subleading block is not periodic, unlike the leading thermal answer.

Load-bearing premise

The closed forms rest on a power-counting argument that only single and double Virasoro raising modes can contribute at order $1/c$, justified by noting that a correlator with $2k$ stress-tensor insertions can gain at most $c^k$ from coincident-operator singularities; no systematic proof is given that triple and higher modes are absent at this order.

Editorial extensions

If this is right

The vacuum block is now known to two orders beyond the semi-classical limit, giving a concrete target for any proposed bulk dual computation of subleading heavy-light blocks in AdS$_3$.
Because the $h_L/c$ term survives in $\log V$ only at order $c^0$, it is a genuine quantum (loop) effect in the bulk, so its explicit form is a check on one-loop gravity in a BTZ or deficit-angle background.
The non-trivial Euclidean-time monodromy of the corrections shows that perturbative $1/c$ physics alone cannot restore the thermal periodicity of the full correlator; only effects of order $e^{-O(c)}$ can.
The integral formulas extend beyond the vacuum block to general heavy-light Virasoro blocks, so the same projector technique can be pushed to higher orders in $1/c$ and to non-vacuum exchange.
The observed near-agreement of the correction functions at small $h_H/c$ and at infinite temperature is attributed to BTZ being locally pure AdS$_3$, suggesting a geometric reason that survives away from both limits.

Reading between the lines

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

If the mode-truncation counting is right, the same projector-plus-contour method should give the $1/c^2$ term mechanically, so the real bottleneck for a systematic expansion is bookkeeping rather than a new idea.
The claim that monodromies cancel between blocks is testable in principle: in a theory with a large gap, the leading OPE singularities are vacuum-block only, so the $1/c$ corrections computed here should be visible in the OPE coefficients of double-trace operators built from the light field.
The resemblance between the small-$h_H/c$ and infinite-temperature corrections hints that a single function of the ratio of the two scales may organize the whole $1/c$ series, which would be worth checking at the next order.

Original abstract

Black hole microstates and their approximate thermodynamic properties can be studied using heavy-light correlation functions in AdS/CFT. Universal features of these correlators can be extracted from the Virasoro conformal blocks in CFT2, which encapsulate quantum gravitational effects in AdS3. At infinite central charge c, the Virasoro vacuum block provides an avatar of the black hole information paradox in the form of periodic Euclidean-time singularities that must be resolved at finite c. We compute Virasoro blocks in the heavy-light, large c limit, extending our previous results by determining perturbative 1/c corrections. We obtain explicit closed-form expressions for both the `semi-classical' $h_L^2 / c^2$ and `quantum' $h_L / c^2$ corrections to the vacuum block, and we provide integral formulas for general Virasoro blocks. We comment on the interpretation of our results for thermodynamics, discussing how monodromies in Euclidean time can arise from AdS calculations using `geodesic Witten diagrams'. We expect that only non-perturbative corrections in 1/c can resolve the singularities associated with the information paradox.

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arXiv listing abstract v3. Results and the main claim are underlined; show every role.

Black hole microstates and their approximate thermodynamic properties can be studied using heavy-light correlation functions in AdS/CFT. Universal features of these correlators can be extracted from the Virasoro conformal blocks in CFT2, which encapsulate quantum gravitational effects in AdS3. At infinite central charge c, the Virasoro vacuum block provides an avatar of the black hole information paradox in the form of periodic Euclidean-time singularities that must be resolved at finite c. We compute Virasoro blocks in the heavy-light, large c limit, extending our previous results by determining perturbative 1/c corrections. We obtain explicit closed-form expressions for both the `semi-classical' $h_L^2 / c^2$ and `quantum' $h_L / c^2$ corrections to the vacuum block, and we provide integral formulas for general Virasoro blocks. We comment on the interpretation of our results for thermodynamics, discussing how monodromies in Euclidean time can arise from AdS calculations using `geodesic Witten diagrams'. We expect that only non-perturbative corrections in 1/c can resolve the singularities associated with the information paradox.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Black hole microstates and their approximate thermodynamic properties can be studied using heavy-light correlation functions in AdS/CFT.	background 1.00	0.07	0.03	asserted 0.64
s1	Universal features of these correlators can be extracted from the Virasoro conformal blocks in CFT2, which encapsulate quantum gravitational effects in AdS3.	background 0.99	0.08	0.05	asserted 0.99
s2	At infinite central charge c, the Virasoro vacuum block provides an avatar of the black hole information paradox in the form of periodic Euclidean-time singularities that must be resolved at finite c.	background 0.93	0.10	0.09	asserted 1.00
s3	We compute Virasoro blocks in the heavy-light, large c limit, extending our previous results by determining perturbative 1/c corrections.	contribution 0.99	0.95	0.12	asserted 1.00
s4	We obtain explicit closed-form expressions for both the `semi-classical' $h_L^2 / c^2$ and `quantum' $h_L / c^2$ corrections to the vacuum block, and we provide integral formulas for general Virasoro blocks.	result 0.96	0.97	0.33	asserted 1.00
s5	We comment on the interpretation of our results for thermodynamics, discussing how monodromies in Euclidean time can arise from AdS calculations using `geodesic Witten diagrams'.	interpretation 1.00	0.36	0.06	hedged possibility 0.40
s6	We expect that only non-perturbative corrections in 1/c can resolve the singularities associated with the information paradox.	interpretation 0.71	0.13	0.39	speculative 0.69

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

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sources read

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

Figures

**Figure 3.** This figure depicts a ‘geodesic Witten diagrams’ that can be used to compute a conformal block from AdS [14]. The lines connecting the two light operators to each other and the two heavy operators to each other are both geodesics, while the wavy line designates a propagator whose endpoints have been fixed to these geodesics. The only integrals are over the positions of the bulk-to-bulk propagator along the geodesics. propagators and a single bulk-to-bulk exchange propagator GBB(X, Y ), as pictured in figure 3. But instead of allowing X and Y to range over AdS, we confine these bulk…

**Figure 4.** This figure shows what happens when we analytically continue the external points of a geodesic Witten diagram. As z moves around the cylinder, the heavy and light geodesics must cross, and as they do, the propagator connecting them passes through its short-distance singularity. Note that in d > 2 dimensions this crossing is enforced by geometry, not by topology. This is the origin of the non-trivial monodromy of the conformal block. Similar reasoning leads to a monodromy in Euclidean time for non-vacuum heavy-light Virasoro blocks [20]. schematic form G∆,0(z, z¯) = Z ∞ −∞ dλdλ0Gb∂(−

**Figure 5.** This figure shows gravitational one-loop diagrams in AdS that could contribute to heavy-light Virasoro blocks at order 1/c. In the small hH/c limit, we expect that the two diagrams on the left should correspond with the 1/c effects in equation (2.22). More generally, the pair of diagrams on the left should be equivalent to the pair on the right with bulk propagators computed in the background gravitational field of the heavy operator. section 2. The geodesic Witten diagram technology has not been applied in the presence of perturbative 1/c corrections, so it is not entirely clear…

Figures reproduced from arXiv:1512.03052 by the authors.

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On Information Loss in AdS$_3$/CFT$_2$
hep-th 2016-03 conditional novelty 7.0 of 10

Non-perturbative finite-central-charge effects in Virasoro blocks remove the forbidden singularities that signal information loss in AdS3/CFT2, and appear to alter correlators at times of order the black hole entropy.

Show 19 more citing papers

Black Hole Collapse in the 1/c Expansion
hep-th 2016-03 accept novelty 7.0 of 10

A large-central-charge CFT calculation of a collapsing null shell reproduces Vaidya-AdS3 two-point functions and entanglement entropy growth, with information loss appearing as a leading-order violation of unitarity.
Smoothing the Bouncing-Geodesic Singularity in AdS/CFT
hep-th 2026-11 conditional novelty 6.0 of 10

Finite-c quantum corrections convert sharp complex-time singularity imprints of the black hole interior into smooth Gaussian profiles, while leaving short-distance, OPE-protected singularities intact.
A Matrix View of Holographic Null-State Equations in $d\geq 2$
hep-th 2026-11 conditional novelty 6.0 of 10

The null-state-type CFT equations from black hole holography can be encoded as determinants of banded finite matrices built from sl2 generators, for all levels in d=2 and d=4.
A proposal for 3d quantum gravity and its bulk factorization
hep-th 2022-10 conditional novelty 6.0 of 10

In an effective 3d gravity model, black hole entropy is reproduced as entanglement entropy of edge modes whose symmetry is the quantum semi-group SL_q^+(2,R), matching the Virasoro modular S-matrix to the quantum grou...
Reparametrization modes, shadow operators, and quantum chaos in higher-dimensional CFTs
hep-th 2019-09 conditional novelty 6.0 of 10

The stress-tensor shadow, the reparametrization mode of Schwarzian and 2d CFT studies, and the kinematic-space OPE block are shown to be one object, giving a single closed-form stress-tensor conformal partial wave val...
Low-dimensional de Sitter quantum gravity
hep-th 2019-05 reject novelty 6.0 of 10

De Sitter JT gravity in two dimensions is shown to be an analytic continuation of Euclidean AdS JT gravity, with a proposed matrix-model completion that the authors' later note says rests on a disproved conjecture.
Universal Lowest-Twist in CFTs from Holography
hep-th 2019-03 accept novelty 6.0 of 10

At large central charge, the lowest-twist OPE coefficients of multi-stress-tensor conformal blocks in any dimension depend only on the light operator's dimension and the ratio of heavy operator dimension to central ch...
Probing thermality beyond the diagonal
hep-th 2018-04 conditional novelty 6.0 of 10

Modular bootstrap of torus two-point functions yields the asymptotic mean-squared off-diagonal OPE coefficients in 2d CFTs, showing e^{-S} suppression consistent with the eigenstate thermalization hypothesis.
On thermality of CFT eigenstates
hep-th 2017-05 conditional novelty 6.0 of 10

In 2D conformal field theories, the trace-square distance between a heavy eigenstate's reduced density matrix and the thermal one scales as (subsystem fraction)^8 and vanishes as 1/c^2 at large central charge.
A Numerical Approach to Virasoro Blocks and the Information Paradox
hep-th 2017-03 accept novelty 6.0 of 10

Heavy-light Virasoro blocks decay as t^{-3/2} at late Lorentzian times independent of intermediate dimension, and the naive semiclassical approximation breaks down in a finite Euclidean region enclosing the forbidden ...
On the Late-Time Behavior of Virasoro Blocks and a Classification of Semiclassical Saddles
hep-th 2016-09 conditional novelty 6.0 of 10

The leading semiclassical Virasoro blocks in AdS3/CFT2 all decay exponentially at late times at a rate independent of the internal operator dimension, so heavy semiclassical states do not resolve information loss.
Degenerate Operators and the $1/c$ Expansion: Lorentzian Resummations, High Order Computations, and Super-Virasoro Blocks
hep-th 2016-06 accept novelty 6.0 of 10

Leading 1/c log z corrections to the Virasoro vacuum block exponentiate into a shift of the chaos exponent from 2*pi/beta to (2*pi/beta)(1 + 12/c), and the block is computed explicitly through order 1/c^3.
Holographic conformal blocks from interacting Wilson lines
hep-th 2016-03 conditional novelty 6.0 of 10

Conformal blocks of W_N algebras at large central charge are obtained from a single bulk vertex where Wilson lines in SL(N) representations meet, reproducing known global, W_3, and heavy-light Virasoro blocks.
A theory of reparameterizations for AdS$_3$ gravity
hep-th 2018-08 conditional novelty 5.0 of 10

Pure AdS3 gravity is shown to be equivalent to two copies of the path-integral quantization of the Virasoro coadjoint orbit Diff(S1)/PSL(2,R), a non-modular boundary QFT whose 1/c expansion computes Virasoro blocks.
Exact Virasoro Blocks from Wilson Lines and Background-Independent Operators
hep-th 2016-12 conditional novelty 5.0 of 10

Wilson line networks in sl(2) Chern-Simons theory compute Virasoro conformal blocks exactly, and automatically generate the coordinate system that uniformizes any background state.
Exploring the BTZ bulk with boundary conformal blocks
hep-th 2016-04 conditional novelty 5.0 of 10

The radial position of a field in the BTZ black hole maps to a conformal cross-ratio in a transformed boundary CFT, allowing the bulk field to be extracted from a heavy-light Virasoro conformal block.
Higher-point conformal blocks and entanglement entropy in heavy states
hep-th 2016-01 conditional novelty 5.0 of 10

Higher-point conformal blocks with two heavy operators factorize into products of four-point blocks in the heavy-light limit, and the same factorization reproduces holographic entanglement entropy for many disjoint in...
A Quantum Correction To Chaos
hep-th 2016-01 conditional novelty 5.0 of 10

The Virasoro vacuum block at order 1/c gives a positive shift to the Lyapunov exponent in CFT2, lambda_L = (2 pi / beta)(1 + 12/c), which the authors argue is consistent with the chaos bound.
From global to heavy-light: 5-point conformal blocks
hep-th 2015-12 conditional novelty 5.0 of 10

The five-point global conformal block is computed explicitly and shown, via the Fitzpatrick-Kaplan-Walters heavy-light procedure, to reproduce the previously known five-point perturbative classical block.

How later papers used it

55 later papers cite it

Evidence: substantial. 46 of the citing papers share no author with it, and 8 of those carry a confident label from Pith's citation classifier.

Pith read 10 of the 99 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

1 paper by the same authors is listed below: 1 cited it as support.

Cites it as support 1 of 3 papers with this label · 1 by the same authors

By the same authors

Said that perturbative corrections in G_N are not expected to alter the conclusion that heavy-light Virasoro blocks decay exponentially at late times, and that this paper explicitly demonstrated it to first order.

A Numerical Approach to Virasoro Blocks and the Information Paradox (2017) (same authors) · 0.98 · paraphrased: the licence does not allow quoting

How the literature uses it

55 arXiv papers cite this in 99 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 61 sentences without a confident label

Builds on it 1 paper

This would open up the possibility to understand higher-point Virasoro identity blocks in interesting regimes such as the Regge limit or in configurations with several heavy operators (generalizing [ref] ), which would have many applications.

Six-point functions and collisions in the black hole interior · Conclusion · 0.81

Uses its method or tool 3 papers

As in the bosonic case analyzed in [ref] , we redefine the integral [ref] by removing the divergent term as [equation] Here we have introduced new parameters as [equation] The first few examples for the integral are [equation] The divergent integral is [equation] Taking care of the coordinate transformation from $y$ to $w$ as in [ref] , we use [equation] Here a new parameter $δ$ is introduced by using the ambiguity in the overall normalization at the order of $ϵ^0$.

Superconformal blocks from Wilson lines with loop corrections · Open Wilson line in a supersymmetric conical space · 0.84
The uniformization map is a conformal transformation, which turns out to be extremely useful in expressing a heavy-light correlator of the form $⟨O_H O_H O_L ⋯O_L⟩$ in terms of correlators of light operators up to some multiplicative factors coming from the decoupled heavy sector and conformal transformation rules [ref] .

Behind-the-horizon excitations from a single 2d CFT · Introduction · 0.98
For $N=2$, a four point function in the heavy-light limit can be mapped to a two point function by applying a coordinate transformation as explained in [ref] .

Conformal blocks from Wilson lines with loop corrections · Conclusion and open problems · 0.93

Uses its data or values 1 paper

The functions $f_10$ and $f_01$ are known from the work of [ref] to be

Degenerate Operators and the $1/c$ Expansion: Lorentzian Resummations, High Order Computations, and Super-Virasoro Blocks · Summary of Corrections to the Vacuum Block · 0.92

Compares with it 9 papers

These special cases agree precisely with our more general results [ref] as $c →∞$, and in particular, exhibit forbidden singularities in the large central charge limit.

On Information Loss in AdS$_3$/CFT$_2$ · A Universal Piece of the Resolution · 0.81
One of the main features of our result is that, for the whole correlator, this holds even at the leading order in the large $c$ limit, while, in the same limit, the contribution of the Virasoro identity block in the $(O_H O_H) (O_L O_L)$ OPE develops spurious singularities [ref] .

Correlators at large c without information loss · Discussion · 0.85
The $1/c$ correction to the block was computed in [ref] , and the $1/c$ correction to $⟨ℬ⟩$ was computed in [ref] ; the two agree.

Scrambling in nearly thermalized states at large central charge · Introduction · 0.97

Cites it as support 2 papers

Fortunately, in all CFT$_2$ there is a universal contribution to each heavy-light correlator, the Virasoro vacuum block [ref] , which manifests information loss in the large central charge or $c →∞$ limit [ref] .

On Information Loss in AdS$_3$/CFT$_2$ · A Universal Piece of the Resolution · 0.96
We do not expect that perturbative corrections in $G_N = 3/2c$ will alter this conclusion, and to first order this has been demonstrated explicitly [ref] .

A Numerical Approach to Virasoro Blocks and the Information Paradox · Implications for Information Loss and the Bootstrap · 0.98

Cites it as background 19 papers

A partial list of examples are Cardy formula [ref] , understanding physics related to ETH/black hole thermality [ref] , chaos at large central charge CFTs with sparse low lying spectrum [ref] , identifying the irrational behavior in large $m$ minimal models [ref] .

Universality in asymptotic bounds and its saturation in $2$D CFT · Introduction & Summary · 0.90
In this paper and other recent work [ref] we have been developing an understanding of black hole thermodynamics, information loss, and its resolution in AdS$_3$/CFT$_2$.

On the Late-Time Behavior of Virasoro Blocks and a Classification of Semiclassical Saddles · Comments on the Generality of Our Results · 0.80
Classical (large-$c$) conformal blocks have been studied in the Riemann sphere, where they were identified with lengths of geodesic networks embedded in the asymptotic AdS spacetime with the angle deficit or BTZ black hole [ref] .

Semiclassical torus blocks in the t-channel · Introduction · 0.94

Discussion

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