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Segal axioms and resolution of Liouville conformal field theory

By Colin Guillarmou

Appears in collection : Geometry and analysis on non-compact manifolds / Géométrie et analyse sur les variétés non compactes

Liouville conformal field theory is a 2 dimensional field theory introduced in physics in the 80's. Here we give a probabilistic construction of the amplitudes of Riemann surfaces with boundary for this field theory, and we prove that they satisfy the so called Segal Axioms. This allows to decompose the correlation function of the theory using the diagonalisation of a certain operator, the Hamiltonian, using scattering theory. One can then show the formulas conjectured in physics in terms of conformal blocks. The spectral analysis, although in an infinite dimensional setting, has some similarities with scattering theory on symmetric spaces. This is joint work with Kupiainen, Rhodes and Vargas.

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Citation data

  • DOI 10.24350/CIRM.V.19902103
  • Cite this video Guillarmou Colin (3/28/22). Segal axioms and resolution of Liouville conformal field theory. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19902103
  • URL https://dx.doi.org/10.24350/CIRM.V.19902103

Bibliography

  • GUILLARMOU, Colin, KUPIAINEN, Antti, RHODES, Rémi, et al. Conformal bootstrap in Liouville theory. arXiv preprint arXiv:2005.11530, 2020. - https://arxiv.org/abs/2005.11530
  • GUILLARMOU, Colin, KUPIAINEN, Antti, RHODES, Rémi, et al. Segal's axioms and bootstrap for Liouville Theory. arXiv preprint arXiv:2112.14859, 2021. - https://arxiv.org/abs/2112.14859

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