Paper Citation Record · LEDGER

Virasoro OPE and Conformal Blocks from the Inverse Shapovalov Form

As of 10 August 2026, this Paper Citation Record lists 49 of 49 outbound references and 0 inbound Pith citation observations for arXiv:2509.09765.

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pith.paper-citation-record.v1
2509.09765 v2

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measured 49 of 49 reference resolution

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measured 49 of 49 standing notices

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Outbound references

Observation f1e49bd4-2abd-4a55-b726-afb94417f4c6 · outbound

This paper cites The Virasoro Completeness Relation and Inverse Shapovalov Form.

Virasoro OPE and Conformal Blocks from the Inverse Shapovalov Form The Virasoro Completeness Relation and Inverse Shapovalov Form

Reference 1

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Observation a119ae84-e55f-44eb-81b0-dde89e664ef5 · outbound

This paper cites Infinite Conformal Symmetry in Two-Dimensional Quantum Field Theory.

Virasoro OPE and Conformal Blocks from the Inverse Shapovalov Form Infinite Conformal Symmetry in Two-Dimensional Quantum Field Theory

Reference 2

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Observation 56659be5-c30f-4123-ad09-da657963ec38 · outbound

This paper cites Conformal field theory on the plane.

Virasoro OPE and Conformal Blocks from the Inverse Shapovalov Form Conformal field theory on the plane

Reference 3

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Observation 0035807f-005f-415d-89b0-8a18a3fce404 · outbound

This paper cites A guide to two-dimensional conformal field theory.

Virasoro OPE and Conformal Blocks from the Inverse Shapovalov Form A guide to two-dimensional conformal field theory

Reference 4

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Observation a35979c6-19ae-4af4-be8b-d6f1a996148f · outbound

This paper cites Modern Approach to 2D Conformal Field Theory.

Virasoro OPE and Conformal Blocks from the Inverse Shapovalov Form Modern Approach to 2D Conformal Field Theory

Reference 5

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Observation 442dce70-edca-4bb8-b11e-effd88e32005 · outbound

This paper cites Conformal Field Theory and Statistical Mechanics.

Virasoro OPE and Conformal Blocks from the Inverse Shapovalov Form Conformal Field Theory and Statistical Mechanics

Reference 6

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Observation fb5efa57-1ff0-4513-bf94-444b2dff0621 · outbound

This paper cites String theory. Vol. 1: An introduction to the bosonic string; String theory. Vol. 2: Superstring theory and beyond.

Virasoro OPE and Conformal Blocks from the Inverse Shapovalov Form String theory. Vol. 1: An introduction to the bosonic string; String theory. Vol. 2: Superstring theory and beyond

Reference 7

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Observation fd72cdb1-ce2f-4dc6-87a9-ca9f2c748368 · outbound

This paper cites Integrable Structure of Conformal Field Theory, Quantum KdV Theory and Thermodynamic Bethe Ansatz.

Virasoro OPE and Conformal Blocks from the Inverse Shapovalov Form Integrable Structure of Conformal Field Theory, Quantum KdV Theory and Thermodynamic Bethe Ansatz

Reference 8

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Observation eb12e3f2-d3e7-4fd6-b790-9323291fdeb4 · outbound

This paper cites Holography from Conformal Field Theory.

Virasoro OPE and Conformal Blocks from the Inverse Shapovalov Form Holography from Conformal Field Theory

Reference 9

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Observation 42d1aee9-583f-4c87-a994-b707de7a76e7 · outbound

This paper cites Entanglement Entropy at Large Central Charge.

Virasoro OPE and Conformal Blocks from the Inverse Shapovalov Form Entanglement Entropy at Large Central Charge

Reference 10

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Observation 5eafd1aa-fd51-442a-b3f9-6c1a3c23ab6a · outbound

This paper cites Virasoro Conformal Blocks and Thermality from Classical Background Fields.

Virasoro OPE and Conformal Blocks from the Inverse Shapovalov Form Virasoro Conformal Blocks and Thermality from Classical Background Fields

Reference 11

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Observation e0c78f7b-6e21-42a7-9818-0ac60a349224 · outbound

This paper cites Conformal Field Theory, 2-DQuantum Gravity and Quantization of Teichmuller Space.

Virasoro OPE and Conformal Blocks from the Inverse Shapovalov Form Conformal Field Theory, 2-DQuantum Gravity and Quantization of Teichmuller Space

Reference 12

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Observation 89fbee19-4824-4cd6-a7a0-d30e126c5b79 · outbound

This paper cites Solving 3d Gravity with Virasoro TQFT.

Virasoro OPE and Conformal Blocks from the Inverse Shapovalov Form Solving 3d Gravity with Virasoro TQFT

Reference 13

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Observation 6f92038c-3758-4e3d-bf63-85f1b3da3e81 · outbound

This paper cites A microscopic realization of dS$_3$.

Virasoro OPE and Conformal Blocks from the Inverse Shapovalov Form A microscopic realization of dS$_3$

Reference 14

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Observation 09098a05-7ac9-442c-a71d-c136315fd75f · outbound

This paper cites Conformal symmetry in two-dimensions: An explicit recurrence formula for the conformal partial wave amplitude.

Virasoro OPE and Conformal Blocks from the Inverse Shapovalov Form Conformal symmetry in two-dimensions: An explicit recurrence formula for the conformal partial wave amplitude

Reference 15

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Observation d1eebeb3-1455-4476-8f5d-8f7879259ac3 · outbound

This paper cites Conformal symmetry in two-dimensional space: Recursion representation of conformal block.

Virasoro OPE and Conformal Blocks from the Inverse Shapovalov Form Conformal symmetry in two-dimensional space: Recursion representation of conformal block

Reference 16

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Observation a598a137-a79b-4964-9ca6-e87c87146782 · outbound

This paper cites Virasoro conformal blocks in closed form.

Virasoro OPE and Conformal Blocks from the Inverse Shapovalov Form Virasoro conformal blocks in closed form

Reference 17

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Observation 337a05f4-f6f6-4bc7-bef7-2867ee136c11 · outbound

This paper cites Recursive Representations of Arbitrary Virasoro Conformal Blocks.

Virasoro OPE and Conformal Blocks from the Inverse Shapovalov Form Recursive Representations of Arbitrary Virasoro Conformal Blocks

Reference 18

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Observation 70593913-be14-4d23-bed1-bf2d33cbc10c · outbound

This paper cites Liouville Correlation Functions from Four-dimensional Gauge Theories.

Virasoro OPE and Conformal Blocks from the Inverse Shapovalov Form Liouville Correlation Functions from Four-dimensional Gauge Theories

Reference 19

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Observation e661f0e1-0f9f-49cd-a45c-7ac2d49bcf52 · outbound

This paper cites On combinatorial expansion of the conformal blocks arising from AGT conjecture.

Virasoro OPE and Conformal Blocks from the Inverse Shapovalov Form On combinatorial expansion of the conformal blocks arising from AGT conjecture

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-04T18:52:23.404666Z

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Observation 2ad3ab6b-8216-4c40-b731-65f3feae5386 · outbound

This paper cites Contravariant form for infinite-dimensional Lie algebras and superalgebras.

Virasoro OPE and Conformal Blocks from the Inverse Shapovalov Form Contravariant form for infinite-dimensional Lie algebras and superalgebras

Reference 21

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Observation f6e38ed1-635e-43f7-81e4-7861381da045 · outbound

This paper cites Higher Equations of Motion in Liouville Field Theory.

Virasoro OPE and Conformal Blocks from the Inverse Shapovalov Form Higher Equations of Motion in Liouville Field Theory

Reference 22

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Observation 550d6f62-f8b9-4517-b9f9-34278f6c06f7 · outbound

This paper cites Norms of logarithmic primaries of Virasoro algebra.

Virasoro OPE and Conformal Blocks from the Inverse Shapovalov Form Norms of logarithmic primaries of Virasoro algebra

Reference 23

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Observation 88aa3be7-bf80-49d5-8178-022913212232 · outbound

This paper cites Degenerate Conformal Field Theories and Explicit Expression for Some Null Vectors.

Virasoro OPE and Conformal Blocks from the Inverse Shapovalov Form Degenerate Conformal Field Theories and Explicit Expression for Some Null Vectors

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-04T18:52:23.421555Z

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Observation 6d56f07c-7858-4ed6-bec3-47b22c6d7997 · outbound

This paper cites Covariant differential equations and singular vectors in Virasoro representations.

Virasoro OPE and Conformal Blocks from the Inverse Shapovalov Form Covariant differential equations and singular vectors in Virasoro representations

Reference 25

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Observation 3061986c-af44-4f76-b2dc-4df2b51ce74a · outbound

This paper cites Virasoro singular vectors.

Virasoro OPE and Conformal Blocks from the Inverse Shapovalov Form Virasoro singular vectors

Reference 26

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Observation e601109d-a91a-4ada-8068-5c3f946be084 · outbound

This paper cites Explicit expressions for Virasoro singular vectors.

Virasoro OPE and Conformal Blocks from the Inverse Shapovalov Form Explicit expressions for Virasoro singular vectors

Reference 27

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Observation 102e4fef-583a-4e73-b89b-8045312545fa · outbound

This paper cites Properties of dual multiloop amplitudes.

Virasoro OPE and Conformal Blocks from the Inverse Shapovalov Form Properties of dual multiloop amplitudes

Reference 28

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Observation ca4d3370-e5af-439e-9736-34cd6a18ba7c · outbound

This paper cites Sewing Conformal Field Theories.

Virasoro OPE and Conformal Blocks from the Inverse Shapovalov Form Sewing Conformal Field Theories

Reference 29

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Observation 834463ba-51a3-461e-a22d-3ff7a5efb3e8 · outbound

This paper cites Conformal Algebra and Multipoint Correlation Functions in Two-Dimensional Statistical Models.

Virasoro OPE and Conformal Blocks from the Inverse Shapovalov Form Conformal Algebra and Multipoint Correlation Functions in Two-Dimensional Statistical Models

Reference 30

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Observation d256b67c-8b76-4327-9b17-364d2c6e9036 · outbound

This paper cites Four Point Correlation Functions and the Operator Algebra in the Two-Dimensional Conformal Invariant Theories with the Central Charge c<1.

Virasoro OPE and Conformal Blocks from the Inverse Shapovalov Form Four Point Correlation Functions and the Operator Algebra in the Two-Dimensional Conformal Invariant Theories with the Central Charge c<1

Reference 31

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Observation 2c0c6da0-e0db-4638-87d9-2fde4b0d4155 · outbound

This paper cites On the $1/c$ expansion in $2d$ CFTs with degenerate operators.

Virasoro OPE and Conformal Blocks from the Inverse Shapovalov Form On the $1/c$ expansion in $2d$ CFTs with degenerate operators

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-04T18:52:23.453986Z

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Observation 50af4a79-ce6c-4c1a-9595-dd056501f978 · outbound

This paper cites Structure Constants and Conformal Bootstrap in Liouville Field Theory.

Virasoro OPE and Conformal Blocks from the Inverse Shapovalov Form Structure Constants and Conformal Bootstrap in Liouville Field Theory

Reference 33

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Observation 22d51d38-e9bd-4e36-a8c3-88a39546329f · outbound

This paper cites Classical Conformal Blocks and Painleve VI.

Virasoro OPE and Conformal Blocks from the Inverse Shapovalov Form Classical Conformal Blocks and Painleve VI

Reference 34

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Observation 0b246677-e5ce-48aa-8963-9547913b49bb · outbound

This paper cites Universality of Long-Distance AdS Physics from the CFT Bootstrap.

Virasoro OPE and Conformal Blocks from the Inverse Shapovalov Form Universality of Long-Distance AdS Physics from the CFT Bootstrap

Reference 35

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Observation d7afa5e9-a72d-4302-b235-6f10c3d7f7a9 · outbound

This paper cites Virasoro vacuum block at next-to-leading order in the heavy-light limit.

Virasoro OPE and Conformal Blocks from the Inverse Shapovalov Form Virasoro vacuum block at next-to-leading order in the heavy-light limit

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-04T18:52:23.469755Z

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Observation 92cc17d9-0502-4315-a219-379cac8cb752 · outbound

This paper cites Degenerate Operators and the $1/c$ Expansion: Lorentzian Resummations, High Order Computations, and Super-Virasoro Blocks.

Virasoro OPE and Conformal Blocks from the Inverse Shapovalov Form Degenerate Operators and the $1/c$ Expansion: Lorentzian Resummations, High Order Computations, and Super-Virasoro Blocks

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-04T18:52:23.473734Z

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Observation 20dbd227-db19-4db5-a481-4ec99b4092ce · outbound

This paper cites A conformal block Farey tail.

Virasoro OPE and Conformal Blocks from the Inverse Shapovalov Form A conformal block Farey tail

Reference 38

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Observation c1d23a9d-3282-4f19-a3eb-5fa33dd70e0b · outbound

This paper cites Large $c$ Virasoro Blocks from Monodromy Method beyond Known Limits.

Virasoro OPE and Conformal Blocks from the Inverse Shapovalov Form Large $c$ Virasoro Blocks from Monodromy Method beyond Known Limits

Reference 39

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Observation e033f164-affe-4562-b4f9-a988b41aeff7 · outbound

This paper cites Four-point conformal blocks with three heavy background operators.

Virasoro OPE and Conformal Blocks from the Inverse Shapovalov Form Four-point conformal blocks with three heavy background operators

Reference 40

Resolution: unresolved; no resolver link, observed 2026-08-04T18:52:23.485931Z

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Observation c3f9e214-f9d1-4794-bf94-2046e4c19722 · outbound

This paper cites A note on the large-$c$ conformal block asymptotics and $\alpha$-heavy operators.

Virasoro OPE and Conformal Blocks from the Inverse Shapovalov Form A note on the large-$c$ conformal block asymptotics and $\alpha$-heavy operators

Reference 41

Resolution: unresolved; no resolver link, observed 2026-08-04T18:52:23.490044Z

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Observation 809804b1-9dcb-4cf3-8607-54b487141a53 · outbound

This paper cites Liouville theory with a central charge less than one.

Virasoro OPE and Conformal Blocks from the Inverse Shapovalov Form Liouville theory with a central charge less than one

Reference 42

Resolution: unresolved; no resolver link, observed 2026-08-04T18:52:23.494104Z

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Observation c82ce470-e05b-479c-bef0-3309244e69fc · outbound

This paper cites Two-dimensional conformal symmetry and critical four-spin correlation functions in the Ashkin-Teller model.

Virasoro OPE and Conformal Blocks from the Inverse Shapovalov Form Two-dimensional conformal symmetry and critical four-spin correlation functions in the Ashkin-Teller model

Reference 43

Resolution: unresolved; no resolver link, observed 2026-08-04T18:52:23.498031Z

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Observation a3c9b677-8919-4201-9409-467b719bd73e · outbound

This paper cites Semi-classical Virasoro blocks: proof of exponentiation.

Virasoro OPE and Conformal Blocks from the Inverse Shapovalov Form Semi-classical Virasoro blocks: proof of exponentiation

Reference 44

Resolution: unresolved; no resolver link, observed 2026-08-04T18:52:23.501856Z

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Observation 82e3b0cd-b26e-4d29-ad1d-24346f7f4d6b · outbound

This paper cites Hawking from Catalan.

Virasoro OPE and Conformal Blocks from the Inverse Shapovalov Form Hawking from Catalan

Reference 45

Resolution: unresolved; no resolver link, observed 2026-08-04T18:52:23.505833Z

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Observation d923d57d-a5bf-441d-831a-fb28ce99f516 · outbound

This paper cites Modular crossings, OPE coefficients and black holes.

Virasoro OPE and Conformal Blocks from the Inverse Shapovalov Form Modular crossings, OPE coefficients and black holes

Reference 46

Resolution: unresolved; no resolver link, observed 2026-08-04T18:52:23.509714Z

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Observation 5008f1b7-dfb2-4e7e-b7e2-c25d59671fef · outbound

This paper cites Casimirs of the Virasoro Algebra.

Virasoro OPE and Conformal Blocks from the Inverse Shapovalov Form Casimirs of the Virasoro Algebra

Reference 47

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Observation 6698ea3b-c74a-4fd4-a789-ffd1326c88b6 · outbound

This paper cites The theory of the double gamma function.

Virasoro OPE and Conformal Blocks from the Inverse Shapovalov Form The theory of the double gamma function

Reference 48

Resolution: unresolved; no resolver link, observed 2026-08-04T18:52:23.518540Z

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Observation ae3164af-4969-4982-a9d1-25bfb36176fb · outbound

This paper cites Notes on crossing transformations of Virasoro conformal blocks.

Virasoro OPE and Conformal Blocks from the Inverse Shapovalov Form Notes on crossing transformations of Virasoro conformal blocks

Reference 49

Resolution: unresolved; no resolver link, observed 2026-08-04T18:52:23.522577Z

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