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In 1987 Graeme Segal gave a functorial definition of Conformal Field Theory (CFT) that was designed to capture the mathematical essence of the Conformal Bootstrap formalism pioneered in physics by Belavin-Polyakov-Zamolodchikov.
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Quantum Backlund transformation for the Liouville theory
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T. Curtright and C. Thorn · 1982
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A.A. Belavin, A.M. Polyakov, and A.B. Zamolodchikov · 1984
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D. Friedan and S. Shenker · 1987
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Geometric Complex Coordinates for Teichmüller Space, in Mathematical Aspects of String Theory
A. Marden · 1987
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Conformal invariants for determinants of Laplacians on Riemann surfaces
W.I. Weisberger · 1987
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Vertex Operator Algebras and the monster
I. Frenkel, J. Lepowsky, and A. Meurman · 1988
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Fractal structure of 2d quantum gravity
V.. Knizhnik, A. Polyakov, and A. Zamolodchikov · 1988
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Extremals of determinants of Laplacians
B Osgood, R Phillips, and P Sarnak · 1988
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The definition of conformal field theory
G. B. Segal · 1988
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Sewing conformal field theories ii
H. Sonoda · 1988
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Horocyclic coordinates for Riemann surfaces and moduli spaces. I. Teichmüller and Riemann spaces of Kleinian groups
I. Kra · 1990
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The hyperbolic metric and the geometry of the universal curve
S. Wolpert · 1990
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Meyer-Vietoris type formula for determinants of elliptic differential operators
D. Burghelea, L. Friedlander, and T. Kappeler · 1992
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Two- and three-point functions in Liouville theory
H. Dorn and H.-J. Otto · 1994
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Determinants of elliptic pseudo-differential operators
M. Kontsevich and S. Vishik · 1994
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Lectures on conformal field theory
K. Gawedzki · 1996
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Zeta regularized products and functional determinants on spheres
J.R. Quine and J. Choi · 1996
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Conformal bootstrap in Liouville field theory
A. Zamolodchikov and Al. Zamolodchikov · 1996
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Two-Dimensional Conformal Geometry and Vertex Operator Algebras
Y.-Z. Huang · 1997
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Traces and Determinants of Linear Operators
I. Gohberg, S. Goldberg, and N. Krupnik · 2000
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Liouville theory revisited
J. Teschner · 2001
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Déterminant relatif et la fonction Xi
G. Carron · 2002
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Three-point function in the minimal Liouville gravity
Al. Zamolodchikov · 2005
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Transition amplitudes and sewing properties for bosons on the Riemann sphere
J. Dimock · 2007
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P ( ϕ ) 2 P(\phi)_{2} quantum field theories and Segal’s axioms
D. Pickrell · 2008
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From quarks to strings, 2008
A. M. Polyakov · 2008
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Nonrational conformal field theory
J. Teschner · 2009
Integrability of Liouville theory: proof of the DOZZformula
A. Kupiainen, R. Rhodes, and V. Vargas · 2020
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The Fyodorov-Bouchaud formula and Liouville conformal field theory
G. Remy · 2020
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Liouville quantum gravity as a mating of trees
B. Duplantier, J. Miller, and S. Sheffield · 2021
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Existence and uniqueness of the Liouville quantum gravity metric for γ ∈ ( 0 , 2 ) \gamma\in(0,2)
E. Gwynne and J. Miller · 2021
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Integrability of boundary Liouville conformal field theory
G. Remy and T. Zhu · 2022
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Conformal Bootstrap on the Annulus in Liouville CFT
B. Wu · 2022
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Plumbing coordinates on Teichmüller space: A counterexample
V. Hinich · 2010
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Augmented Teichmüller spaces and orbifolds
V Hinich and A. Vaintrob · 2010
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Quantization of the Hitchin moduli spaces, Liouville theory and the geometric Langlands correspondence I
J. Teschner · 2011
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Holomorphic plumbing coordinates
C. Earle and A. Marden · 2012
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Conformal loop ensembles: the Markovian characterization and the loop-soup construction
S. Sheffield and W. Werner · 2012
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FZZ formula of boundary Liouville CFT via conformal welding
M. Ang, G. Remy, and X. Sun · 2023
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Derivation of all structure constants for boundary Liouville CFT
M. Ang, G. Remy, X. Sun, and T. Zhu · 2023
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Probabilistic construction of Toda Conformal Field Theories
B. Cerclé, R. Rhodes, and V. Vargas · 2023
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Compactified imaginary Liouville theory
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R. Ghosal, G. Remy, X. Sun, and Y. Sun · 2023
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Convergence of uniform triangulations under the cardy embedding
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Integrability of conformal loop ensemble: Imaginary dozz formula and beyond
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The Virasoro structure and the scattering matrix for Liouville conformal field theory
G. Baverez, C. Guillarmou, A. Kupiainen, R. Rhodes, and V. Vargas · 2024
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Semigroup of annuli in Liouville CFT
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Three-point correlation functions in the 𝔰 𝔩 3 \mathfrak{sl}_{3} Toda theory II: the Fateev-Litvinov formula
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Review on the probabilistic construction and conformal bootstrap in Liouville theory
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Conformal bootstrap in Liouville Theory
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Probabilistic conformal blocks for Liouville CFT on the torus
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Conformal Bootstrap for surfaces with boundary in Liouville CFT. Part 1: Segal axioms
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Sewing and propagation of conformal blocks
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The conformal blocks of Liouville CFT
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Conformal Bootstrap for surfaces with boundary in Liouville CFT. Part 2: Spectral resolution and Ward identity
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