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 [“...

Full description

Saved in:
Bibliographic Details
Published in:Journal of mathematical physics 2016-02, Vol.57 (2), p.1
Main Authors: David, François, Rhodes, Rémi, Vargas, Vincent
Format: Article
Language:English
Subjects:
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
CONFORMAL INVARIANCE
Field theory
Gravity
Linear equations
Mathematical Physics
Mathematical problems
Mathematics
Physicists
Physics
Polyhedra
Probability
Quantum field theory
QUANTUM GRAVITY
Quantum theory
RANDOMNESS
Riemann manifold
RIEMANN SPACE
Spheres
TOPOLOGY
TORI
Toruses
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.4938107