Higher equations of motion at level 2 in Liouville CFT
Abstract: In a previous work, we investigated the analytic continuation of the bulk Poisson operator of Liouville conformal field theory on the holomorphic part of Fock space and used it to construct irreducible representations of the Virasoro algebra at the degenerate values of the conformal weights. Here, we study two cases where the Poisson operator admits some simple poles on the Kac table: the bulk Poisson operator on the full Fock space (both holomorphic and anti-holomorphic part), and the boundary Poisson operator on the Fock space. As a consequence, the derivative of top singular vector does not vanish, and we can identify it with a scalar multiple of a primary field of same conformal weight. These are known as higher-equations of motions in physics and have been studied in connection with minimal gravity.
- Integrability of SLE via conformal welding of random surfaces. arXiv e-prints, page arXiv:2104.09477, April 2021.
- Morris Ang. Liouville conformal field theory and the quantum zipper. arXiv e-prints, page arXiv:2301.13200, January 2023.
- Probabilistic derivation of higher equations of motion in Liouville CFT. Manuscript available on the webpage of the authors.
- Derivation of all structure constants for boundary Liouville CFT. arXiv e-prints, page arXiv:2305.18266, May 2023.
- Guillaume Baverez. Modular bootstrap agrees with the path integral in the large moduli limit. Electron. J. Probab., 24:Paper No. 144, 22, 2019.
- A. Belavin and V. Belavin. Higher equations of motion in boundary Liouville field theory. J. High Energy Phys., (2):010, 18, 2010.
- The Virasoro structure and the scattering matrix for Liouville conformal field theory. to appear in Probability and Mathematical Physics, 2023.
- Infinite conformal symmetry in two-dimensional quantum field theory. Nuclear Physics B, 241(2):333–380, 1984.
- Fusion asymptotics for Liouville correlation functions. arXiv e-prints, page arXiv:1807.10207, July 2018.
- Irreducibility of Virasoro representations in Liouville CFT. arXiv e-prints, page arXiv:2312.07344, December 2023.
- Integrals over a moduli space, the ring of discrete states, and a four-point function in minimal Liouville gravity. Teoret. Mat. Fiz., 147(3):339–371, 2006.
- Baptiste Cerclé. Belavin-Polyakov-Zamolodchikov differential equations for boundary Liouville conformal field theory from the Ward identities. in preparation.
- Conformal field theory. Graduate Texts in Contemporary Physics. Springer-Verlag, New York, 1997.
- Liouville quantum gravity on the Riemann sphere. Comm. Math. Phys., 342(3):869–907, 2016.
- Renormalizability of Liouville quantum field theory at the Seiberg bound. Electron. J. Probab., 22:Paper No. 93, 26, 2017.
- Liouville quantum gravity as a mating of trees. Astérisque, (427):viii+257, 2021.
- Liouville quantum gravity on complex tori. J. Math. Phys., 57(2):022302, 25, 2016.
- The importance of the Selberg integral. Bull. Amer. Math. Soc. (N.S.), 45(4):489–534, 2008.
- Boundary Liouville Field Theory I. Boundary State and Boundary Two-point Function. arXiv e-prints, pages hep–th/0001012, January 2000.
- Conformal bootstrap in Liouville Theory. to appear in Acta Mathematica, 2023.
- Polyakov’s formulation of 2d2𝑑2d2 italic_d bosonic string theory. Publ. Math. Inst. Hautes Études Sci., 130:111–185, 2019.
- Conformal bootstrap for open surfaces in Liouville conformal field theory. in preparation.
- Jean-Pierre Kahane. Sur le chaos multiplicatif. Ann. Sci. Math. Québec, 9(2):105–150, 1985.
- Local conformal structure of Liouville quantum gravity. Comm. Math. Phys., 371(3):1005–1069, 2019.
- Integrability of Liouville theory: proof of the DOZZ formula. Ann. of Math. (2), 191(1):81–166, 2020.
- Yury A. Neretin. On the Dotsenko-Fateev complex twin of the Selberg integral and its extensions. arXiv e-prints, page arXiv:2212.09112, December 2022.
- Graeme Segal. The definition of conformal field theory. In Topology, geometry and quantum field theory, volume 308 of London Math. Soc. Lecture Note Ser., pages 421–577. Cambridge Univ. Press, Cambridge, 2004.
- J Teschner. Liouville theory revisited. Classical and Quantum Gravity, 18(23):R153–R222, nov 2001.
- A. Zamolodchikov. Higher equations of motion in Liouville field theory. Int. J. Mod. Phys. A, 19S2:510–523, 2004.
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