15. August 2025

Liouville Quantum Gravity

Video Illustrating geodesic balls in a Liouville Quantum Gravity metric at increasing resolution.

Video The Liouville Quantum Gravity measure shown together with a collection of geodesics to a point at the center, again at increasing resolution. It illustrated how geodesics in a quantum geometry tend to merge before reaching their endpoint.

References

[1] Ambjørn, J. and Budd, T.G., 2014. Geodesic distances in Liouville quantum gravity. Nuclear Physics B, 889, pp.676-691.

[2] Ding, Jian, Julien Dubédat, Alexander Dunlap, and Hugo Falconet. “Tightness of Liouville first passage percolation for γ∈(0, 2).” Publications mathématiques de l’IHÉS 132, no. 1 (2020): 353-403.

[3] Dubédat, Julien, Hugo Falconet, Ewain Gwynne, Joshua Pfeffer, and Xin Sun. “Weak LQG metrics and Liouville first passage percolation.” Probability Theory and Related Fields 178, no. 1 (2020): 369-436.

[4] Gwynne, Ewain, and Jason Miller. “Existence and uniqueness of the Liouville quantum gravity metric for γ∈(0, 2).” Inventiones mathematicae 223, no. 1 (2021): 213-333.

[5] Budd, Timothy. “Lessons from the mathematics of two-dimensional Euclidean quantum gravity.” In Handbook of Quantum Gravity, pp. 1-55. Singapore: Springer Nature Singapore, 2023.