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This paper is the first of a series of works on the conformal bootstrap in Liouville conformal field theory (CFT) with boundaries.
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Colin Guillarmou, Laurent Guillopé, The determinant of the Dirichlet-to-Neumann map for surfaces with boundary, International Mathematics Research Notices, Volume 2007, 2007, rnm099
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J. Bettinelli and G. Miermont. Compact Brownian surfaces I: Brownian disks. Probab. Theory Related Fields, 167(3-4):555614, 2017
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François David, Antti Kupiainen, Rémi Rhodes, Vincent Vargas. Renormalizability of Liouville quantum field theory at the Seiberg bound, Electron. J. Probab. 22: 1-26 (2017). DOI: 10.1214/17-EJP113
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Morris Ang, Nina Holden, Xin Sun, Conformal welding of quantum disks, arXiv:2009.08389 [math.PR]
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L. F. Alday, D. Gaiotto, and Y. Tachikawa. Liouville Correlation Functions from Four Dimensional Gauge Theories, Lett. Math. Phys. 91
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V.Belavin,Phys. Torus Amplitudes in Minimal Liouville Gravity and Matrix Models, Lett.B 698 (2011) 86-90
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S. Sheffield, W. Werner: Conformal loop ensembles: the Markovian characterization and the loop-soup construction. Ann. of Math. (2), 176(3):1827–1917, 2012
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Le Gall J.-F., Uniqueness and universality of the Brownian map , Annals of Probability 41
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Miermont G.: The Brownian map is the scaling limit of uniform random plane quadrangulations, Acta Mathematica 210
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David F., Kupiainen A., Rhodes R., Vargas V., Liouville Quantum Gravity on the Riemann sphere, Communications in Mathematical Physics 342
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Huang Y., Rhodes R., Vargas V. Liouville quantum gravity on the unit disk. Ann. Inst. H. Poincaré Probab. Statist. 54(3): 1694-1730 (August 2018)
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Guillaume Remy. Liouville quantum gravity on the annulus. Journal of Mathematical Physics. 59, 082303 (2018)
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Guillarmou C., Rhodes R., Vargas V., Polyakov’s formulation of 2d bosonic string theory, Publications mathématiques de l’IHES 130
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Kupiainen A., Rhodes R., Vargas V., Local conformal structure of Liouville Quantum Gravity, Communications in Mathematical Physics 371
2019
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Guillaume Baverez, Modular bootstrap agrees with the path integral in the large moduli limit, Electron. J. Probab. 24: 1-22 (2019). DOI: 10.1214/19-EJP394
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Kupiainen A., Rhodes R., Vargas V.: Integrability of Liouville theory: proof of the DOZZ formula, Annals of Mathematics 191
2020
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Miller J., Sheffield S.: Liouville quantum gravity and the Brownian map I: The QLE(8/3,0) metric , Inventiones Mathematicae 219
2020
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Kupiainen A., Rhodes R., Vargas V., Integrability of Liouville theory: proof of the DOZZ formula , Annals of Mathematics 191
2020
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Miller J., Sheffield S., Liouville quantum gravity and the Brownian map III: The conformal structure is determined , Probab. Theory Relat. Fields 179
2021
Later among the works it cites.