Liouville theory and the Weil-Petersson geometry of moduli space: bordered, conic, and higher genus surfaces

2023/12/01 by Colville, Kale, Harrison, Sarah M., Maloney, Alexander +1
#FOS: Physical sciences #High Energy Physics - Theory (hep-th)

paper · doi:10.48550/arxiv.2312.00323

Abstract

Two-dimensional conformal field theory is a powerful tool to understand the geometry of surfaces. Here, we study Liouville conformal field theory in the classical (large central charge) limit, where it encodes the geometry of the moduli space of Riemann surfaces. Generalizing previous work, we employ this to study moduli spaces of higher genus surfaces, surfaces with boundaries, and surfaces with cone points. In each case, the knowledge of classical conformal blocks provides an extremely efficient approximation to the Weil-Petersson metric on moduli space. We find detailed agreement with analytic results for volumes and geodesic lengths on moduli space.

Related

• Liouville Theory and the Weil-Petersson Geometry of Moduli Space
• Liouville conformal field theory on Riemann surface with boundaries
• Quasiconformal Teichmuller theory as an analytical foundation for two-dimensional conformal field theory
• Quantization of moduli spaces of flat connections and Liouville theory
• Gluing theory of Riemann surfaces and Liouville conformal field theory