HEP Theory Journal Club

Liouville theory and the Weil–Petersson geometry of moduli space

Keivan Namjou

McGill

Conformal field theory is a powerful tool in the study of geometry, with applications ranging from mirror symmetry to spectral theory and quantum chaos. Liouville theory is a specific conformal field theory that provides a natural means to study the Weil–Petersson geometry of the moduli space of Riemann surfaces. In the semiclassical limit, the Liouville path integral computes the Kähler potential, giving access to the metric and associated geometric quantities. In this talk, I will review Liouville theory, the geometry of hyperbolic surfaces and their moduli space, and explain how the study of Liouville theory in the semiclassical limit allows us to describe these geometries.