# Liouville quantum gravity on complex tori

@article{David2016LiouvilleQG,
title={Liouville quantum gravity on complex tori},
author={Franccois David and R{\'e}mi Rhodes and Vincent Vargas},
journal={Journal of Mathematical Physics},
year={2016},
volume={57},
pages={022302}
}
• Published 2 April 2015
• Mathematics
• 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…

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