05. December 2025

Ideal hyperbolic polygons and the Schwarzian field theory

Random ideal polygons with 12, 24, 48, and 96 sides. In the back the polygons are shown in the Poincare disk, while in the front the radial coordinate is rescaled by a power proportional to the number of sides.
Figure Random ideal polygons with 12, 24, 48, and 96 sides. In the back the polygons are shown in the Poincare disk, while in the front the radial coordinate is rescaled by a power proportional to the number of sides.
Figure Random ideal 40-gons with increasing kappa.
Figure Random ideal 40-gons with increasing kappa.

References

[1] Chekhov, Leonid O. “Fool’s crowns, trumpets, and Schwarzian.” arXiv preprint arXiv:2411.03913 (2024).

[2] Stanford, Douglas, and Edward Witten. “Fermionic localization of the Schwarzian theory.” Journal of High Energy Physics 2017, no. 10 (2017): 1-28.

[3] Bauerschmidt, Roland, Ilya Losev, and Peter Wildemann. “Probabilistic definition of the Schwarzian field theory.” arXiv preprint arXiv:2406.17068 (2024).

Latest Posts