Publication : t15/045

Liouville Quantum Gravity on the complex tori

David F. (CEA, IPhT (Institut de Physique Théorique), F-91191 Gif-sur-Yvette, France)
Rhodes R. (LAMA, Université Paris-Est Marne-la-Vallée, Champs sur Marne, France)
Vargas V. (DMA, Ecole Normale Supérieure, 45 rue d’Ulm, 75005 Paris, France)
In this paper, we construct Liouville Quantum Field Theory (LQFT) on the toroidal topology in the spirit of the 1981 seminal work by Polyakov. Our approach follows the construction carried out by the authors together with A. Kupiainen in the case of the Riemann sphere. The difference is here that the moduli space for complex tori is non trivial. Modular properties of LQFT are thus investigated. This allows us to sum up the LQFT on complex tori over the moduli space, to compute the law of the random Liouville modulus, therefore recovering (and extending) formulae obtained by physicists, and make conjectures about the relationship with random planar maps of genus one, eventually weighted by a conformal field theory and conformally embedded onto the torus.
Année de publication : 2015
Revue : J. Math. Phys. 57 022302 (2016) (2015)
Preprint : arXiv:1504.00625
Lien :
Langue : Anglais

Fichier(s) à télécharger :
  • publi.pdf


    Retour en haut