Renormalizability of Liouville quantum field theory at the Seiberg bound

Abstract : Liouville Quantum Field Theory (LQFT) can be seen as a probabilistic theory of 2d Riemannian metrics e φ(z) |dz| 2 , conjecturally describing scaling limits of discrete 2d-random surfaces. The law of the random field φ in LQFT depends on weights α ∈ R that in classical Riemannian geometry parametrize power law singularities in the metric. A rigorous construction of LQFT has been carried out in [4] in the case when the weights are below the so called Seiberg bound: α < Q where Q parametrizes the random surface model in question. These correspond to studying uniformized surfaces with conical singularities in the classical geometrical setup. An interesting limiting case in classical geometry are the cusp singularities. In the random setup this corresponds to the case when the Seiberg bound is saturated. In this paper, we construct LQFT in the case when the Seiberg bound is saturated which can be seen as the probabilistic version of Riemann surfaces with cusp singularities. The construction involves methods from Gaussian Multiplicative Chaos theory at criticality.
Type de document :
Pré-publication, Document de travail
2017
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https://hal-upec-upem.archives-ouvertes.fr/hal-01587107
Contributeur : Rémi Rhodes <>
Soumis le : mercredi 13 septembre 2017 - 16:29:08
Dernière modification le : mardi 24 avril 2018 - 17:20:06
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  • HAL Id : hal-01587107, version 1
  • ARXIV : 1506.01968

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François David, Antti Kupiainen, Rémi Rhodes, Vincent Vargas. Renormalizability of Liouville quantum field theory at the Seiberg bound. 2017. 〈hal-01587107〉

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