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TMF, 2005, Volume 142, Number 2, Pages 218–234 (Mi tmf1777)  

This article is cited in 54 scientific papers (total in 54 papers)

Three-point function in the minimal Liouville gravity

Al. B. Zamolodchikovab

a Institute for Theoretical and Experimental Physics
b Laboratoire de Physique Mathématique, Université Montpellier II, Montpellier, France

Abstract: We revisit the problem of the structure constants of the operator product expansions in the minimal models of conformal field theory, rederiving these previously known constants and presenting them in a form particularly useful in Liouville gravity applications. We discuss the analytic relation between our expression and the structure constant in the Liouville field theory and also give the three- and two-point correlation numbers on the sphere in the minimal Liouville gravity in the general form.

Keywords: conformal field theory, Liouville gravity, minimal models

DOI: https://doi.org/10.4213/tmf1777

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English version:
Theoretical and Mathematical Physics, 2005, 142:2, 183–196

Bibliographic databases:

Citation: Al. B. Zamolodchikov, “Three-point function in the minimal Liouville gravity”, TMF, 142:2 (2005), 218–234; Theoret. and Math. Phys., 142:2 (2005), 183–196

Citation in format AMSBIB
\by Al.~B.~Zamolodchikov
\paper Three-point function in the minimal Liouville gravity
\jour TMF
\yr 2005
\vol 142
\issue 2
\pages 218--234
\jour Theoret. and Math. Phys.
\yr 2005
\vol 142
\issue 2
\pages 183--196

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    This publication is cited in the following articles:
    1. Gwynne E. Holden N. Pfeffer J. Remy G., “Liouville Quantum Gravity With Matter Central Charge in (1,25): a Probabilistic Approach”, Commun. Math. Phys.  crossref  mathscinet  isi
    2. JETP Letters, 82:1 (2005), 7–13  mathnet  crossref  isi
    3. Al. B. Zamolodchikov, Yu. Ishimoto, “Massive Majorana fermion coupled to two-dimensional gravity and the random-lattice Ising model”, Theoret. and Math. Phys., 147:3 (2006), 755–776  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. JETP Letters, 84:8 (2006), 418–424  mathnet  crossref  isi
    5. A. A. Belavin, Al. B. Zamolodchikov, “Integrals over moduli spaces, ground ring, and four-point function in minimal Liouville gravity”, Theoret. and Math. Phys., 147:3 (2006), 729–754  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    6. Kostov, IK, “Bulk correlation functions in 2d quantum gravity”, Theoretical and Mathematical Physics, 146:1 (2006), 108  mathnet  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    7. Al. B. Zamolodchikov, “Gravitational Yang–Lee model: Four-point function”, Theoret. and Math. Phys., 151:1 (2007), 439–458  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    8. V. A. Belavin, “$N=1$ supersymmetric conformal block recursion relations”, Theoret. and Math. Phys., 152:3 (2007), 1275–1285  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    9. Fateev VA, Litvinov AV, “Coulomb integrals in Liouville theory and Liouville gravity”, JETP Letters, 84:10 (2007), 531–536  mathnet  crossref  adsnasa  isi  scopus  scopus
    10. Kostov, IK, “Non-rational 2D quantum gravity: I. World sheet CFT”, Nuclear Physics B, 770:3 (2007), 273  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    11. Fredenhagen S., Wellig D., “A common limit of super Liouville theory and minimal models”, Journal of High Energy Physics, 2007, no. 9, 098  crossref  mathscinet  isi  scopus  scopus
    12. V. A. Fateev, A. V. Litvinov, “Multipoint correlation functions in Liouville field theory and minimal Liouville gravity”, Theoret. and Math. Phys., 154:3 (2008), 454–472  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    13. Giribet, G, “Comment on three-point function in AdS(3)/CFT(2)”, Journal of Mathematical Physics, 50:4 (2009), 042304  crossref  mathscinet  adsnasa  isi  scopus  scopus
    14. Belavin, AA, “On correlation numbers in 2D minimal gravity and matrix models”, Journal of Physics A-Mathematical and Theoretical, 42:30 (2009), 304004  crossref  mathscinet  zmath  isi  scopus  scopus
    15. Fateev, VA, “A differential equation for a four-point correlation function in Liouville field theory and elliptic four-point conformal blocks”, Journal of Physics A-Mathematical and Theoretical, 42:30 (2009), 304011  crossref  mathscinet  zmath  isi  scopus  scopus
    16. O. V. Alekseev, M. A. Bershtein, “The ring of physical states in the $M(2,3)$ minimal Liouville gravity”, Theoret. and Math. Phys., 164:1 (2010), 929–946  mathnet  crossref  crossref  adsnasa  isi
    17. Belavin A.A., Tarnopolsky G.M., “Introduction to string theory and conformal field theory”, Phys. Atomic Nuclei, 73:5 (2010), 848–877  crossref  adsnasa  isi  elib  scopus  scopus
    18. JETP Letters, 93:2 (2011), 47–51  mathnet  crossref  isi
    19. Ahn Ch., Stanishkov M., Stoilov M., “Higher equations of motion in N=2 superconformal Liouville field theory”, Phys Lett B, 695:5 (2011), 501–506  crossref  mathscinet  adsnasa  isi  elib  scopus  scopus
    20. Alba V.A., Fateev V.A., Litvinov A.V., Tarnopolskiy G.M., “On Combinatorial Expansion of the Conformal Blocks Arising from AGT Conjecture”, Lett Math Phys, 98:1 (2011), 33–64  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    21. Ziff R.M., Simmons J.J.H., Kleban P., “Factorization of correlations in two-dimensional percolation on the plane and torus”, J. Phys. A: Math. Theor., 44:6 (2011), 065002  crossref  mathscinet  zmath  adsnasa  isi  scopus
    22. Gamayun O. Iorgov N. Lisovyy O., “Conformal Field Theory of Painlevé VI”, J. High Energy Phys., 2012, no. 10, 038  crossref  mathscinet  isi  elib  scopus
    23. Picco M. Santachiara R. Viti J. Delfino G., “Connectivities of Potts Fortuin-Kasteleyn Clusters and Time-Like Liouville Correlator”, Nucl. Phys. B, 875:3 (2013), 719–737  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    24. Belavin A.A. Bershtein M.A. Feigin B.L. Litvinov A.V. Tarnopolsky G.M., “Instanton Moduli Spaces and Bases in Coset Conformal Field Theory”, Commun. Math. Phys., 319:1 (2013), 269–301  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    25. Maltz J., “Gauge Invariant Computable Quantities in Timelike Liouville Theory”, J. High Energy Phys., 2013, no. 1, 151  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    26. Delfino G., Picco M., Santachiara R., Viti J., “Spin Clusters and Conformal Field Theory”, J. Stat. Mech.-Theory Exp., 2013, P11011  crossref  mathscinet  isi  scopus  scopus
    27. Belavin A. Dubrovin B. Mukhametzhanov B., “Minimal Liouville Gravity Correlation Numbers From Douglas String Equation”, J. High Energy Phys., 2014, no. 1, 156  crossref  mathscinet  zmath  isi  scopus  scopus
    28. Hadasz L., Jaskolski Z., “Super-Liouville - Double Liouville Correspondence”, J. High Energy Phys., 2014, no. 5, 124  crossref  mathscinet  zmath  isi  scopus  scopus
    29. Santachiara R. Viti J., “Local Logarithmic Correlators as Limits of Coulomb Gas Integrals”, Nucl. Phys. B, 882 (2014), 229–262  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    30. Vasseur R., Jacobsen J.L., “Operator Content of the Critical Potts Model in D Dimensions and Logarithmic Correlations”, Nucl. Phys. B, 880 (2014), 435–475  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    31. Belavin V., “Correlation Functions in Unitary Minimal Liouville Gravity and Frobenius Manifolds”, J. High Energy Phys., 2015, no. 2, 052  crossref  mathscinet  isi  scopus  scopus
    32. Furlan P. Petkova V.B., “on Some 3-Point Functions in the W-4 CFT and Related Braiding Matrix”, J. High Energy Phys., 2015, no. 12, 079, 1–23  crossref  mathscinet  isi  scopus
    33. Aleshkin K. Belavin V., “On the construction of the correlation numbers in Minimal Liouville Gravity”, J. High Energy Phys., 2016, no. 11, 142  crossref  mathscinet  zmath  isi  elib  scopus
    34. Dotsenko V.S., “Correlation function of four spins in the percolation model”, Nucl. Phys. B, 911 (2016), 712–743  crossref  zmath  isi  elib  scopus
    35. Bautista T. Dabholkar A., “Quantum cosmology near two dimensions”, Phys. Rev. D, 94:4 (2016), 044017  crossref  mathscinet  isi  elib  scopus
    36. Dotsenko V.S., “Analytic continuations of 3-point functions of the conformal field theory”, Nucl. Phys. B, 907 (2016), 208–248  crossref  mathscinet  zmath  isi  elib  scopus
    37. Ikhlef Ya. Jacobsen J.L. Saleur H., Phys. Rev. Lett., 116:13 (2016), 130601  crossref  mathscinet  isi  elib  scopus
    38. Maltz J., “de Sitter harmonies: Cosmological spacetimes as resonances”, Phys. Rev. D, 95:6 (2017), 066006  crossref  mathscinet  isi  scopus  scopus
    39. Gori G., Viti J., “Exact Logarithmic Four-Point Functions in the Critical Two-Dimensional Ising Model”, Phys. Rev. Lett., 119:19 (2017), 191601  crossref  isi  scopus  scopus
    40. Giribet G. Rado L., “On Non-Homogeneous Tachyon Condensation in Closed String Theory”, J. High Energy Phys., 2017, no. 8, 015  crossref  mathscinet  isi  scopus  scopus
    41. Behan C., “Unitary Subsector of Generalized Minimal Models”, Phys. Rev. D, 97:9 (2018), 094020  crossref  isi  scopus  scopus
    42. Dupic T. Estienne B. Ikhlef Y., “The Imaginary Toda Field Theory”, J. Phys. A-Math. Theor., 52:10 (2019), 105201  crossref  isi  scopus
    43. Dupic T. Estienne B. Ikhlef Y., “Three-Point Functions in the Fully Packed Loop Model on the Honeycomb Lattice”, J. Phys. A-Math. Theor., 52:20 (2019), 205003  crossref  mathscinet  isi
    44. Kupiainen A. Rhodes R. Vargas V., “Local Conformal Structure of Liouville Quantum Gravity”, Commun. Math. Phys., 371:3 (2019), 1005–1069  crossref  mathscinet  isi
    45. Bautista T. Dabholkar A. Erbin H., “Quantum Gravity From Timelike Liouville Theory”, J. High Energy Phys., 2019, no. 10, 284  crossref  mathscinet  isi
    46. Penedones J., Silva J.A., Zhiboedov A., “Nonperturbative Mellin Amplitudes: Existence, Properties, Applications”, J. High Energy Phys., 2020, no. 8, 031  crossref  mathscinet  isi
    47. Anninos D. Muhlmann B., “Notes on Matrix Models (Matrix Musings)”, J. Stat. Mech.-Theory Exp., 2020:8 (2020), 083109  crossref  mathscinet  isi
    48. Coman I., Pomoni E., Teschner J., “Trinion Conformal Blocks From Topological Strings”, J. High Energy Phys., 2020, no. 9, 78  crossref  mathscinet  isi
    49. Gorbenko V., Zan B., “Two-Dimensional O(N) Models and Logarithmic Cfts”, J. High Energy Phys., 2020, no. 10, 99  crossref  mathscinet  isi
    50. Dotsenko V.S., “Four Spins Correlation Function of the Q States Potts Model, For General Values of Q. Its Percolation Model Limit Q -> 1”, Nucl. Phys. B, 953 (2020), 114973  crossref  mathscinet  isi
    51. Bautista T. Erbin H. Kudrna M., “Brst Cohomology of Timelike Liouville Theory”, J. High Energy Phys., 2020, no. 5, 029  crossref  mathscinet  isi
    52. Javerzat N. Picco M. Santachiara R., “Three- and Four-Point Connectivities of Two-Dimensional Critical Q-Potts Random Clusters on the Torus”, J. Stat. Mech.-Theory Exp., 2020:5 (2020), 053106  crossref  mathscinet  isi
    53. He Y., Jacobsen J.L., Saleur H., “Geometrical Four-Point Functions in the Two-Dimensional Critical Q-State Potts Model: the Interchiral Conformal Bootstrap”, J. High Energy Phys., 2020, no. 12, 19  crossref  mathscinet  isi
    54. Mertens T.G., Turiaci G.J., “Liouville Quantum Gravity - Holography, Jt and Matrices”, J. High Energy Phys., 2021, no. 1, 73  crossref  isi
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