skip to main content

Title: Liouville quantum gravity on complex tori

In this paper, we construct Liouville Quantum Field Theory (LQFT) on the toroidal topology in the spirit of the 1981 seminal work by Polyakov [Phys. Lett. B 103, 207 (1981)]. Our approach follows the construction carried out by the authors together with Kupiainen in the case of the Riemann sphere [“Liouville quantum gravity on the Riemann sphere,” e-print arXiv:1410.7318]. 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 integrate 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.
Authors:
 [1] ;  [2] ;  [3]
  1. Institut de Physique Théorique, CNRS, URA 2306, CEA, IPhT, Gif-sur-Yvette (France)
  2. Université Paris-Est Marne la Vallée, LAMA, Champs sur Marne (France)
  3. ENS Paris, DMA, 45 rue d’Ulm, 75005 Paris (France)
Publication Date:
OSTI Identifier:
22479630
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 57; Journal Issue: 2; Other Information: (c) 2016 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CONFORMAL INVARIANCE; QUANTUM GRAVITY; RANDOMNESS; RIEMANN SPACE; TOPOLOGY; TORI