Classical Liouville action on the sphere with three hyperbolic singularities

TL;DR

This paper derives and analyzes the classical Liouville solution with three hyperbolic singularities on the sphere, explicitly calculating the classical action and confirming its agreement with the quantum three-point function in Liouville theory.

Contribution

It provides an explicit calculation of the classical Liouville action for three hyperbolic singularities, linking classical solutions to quantum three-point functions.

Findings

Explicit classical Liouville solution with three hyperbolic singularities.

Calculated classical Liouville action matches the quantum DOZZ three-point function.

Confirmed the classical limit correspondence in Liouville theory.

Abstract

The classical solution to the Liouville equation in the case of three hyperbolic singularities of its energy-momentum tensor is derived and analyzed. The recently proposed classical Liouville action is explicitly calculated in this case. The result agrees with the classical limit of the three point function in the DOZZ solution of the quantum Liouville theory.