Liouville quantum gravity on complex tori

  title={Liouville quantum gravity on complex tori},
  author={Franccois David and R{\'e}mi Rhodes and Vincent Vargas},
  journal={Journal of Mathematical Physics},
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… 

Liouville quantum gravity on the annulus

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    Journal of Mathematical Physics
  • 2018
In this work we construct Liouville quantum gravity on an annulus in the complex plane. This construction is aimed at providing a rigorous mathematical framework to the work of theoretical physicists

J ul 2 01 8 Liouville quantum gravity on the annulus

In this work we construct Liouville quantum gravity on an annulus in the complex plane. This construction is aimed at providing a rigorous mathematical framework to the work of theoretical physicists


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