Polyakov conjecture for hyperbolic singularities

TL;DR

This paper proposes a specific form of the Liouville action that satisfies the Polyakov conjecture regarding accessory parameters for hyperbolic singularities on the Riemann sphere, advancing understanding in complex analysis and mathematical physics.

Contribution

It introduces a new formulation of the Liouville action consistent with the Polyakov conjecture for hyperbolic singularities.

Findings

Derived the explicit form of the Liouville action

Confirmed the conjecture for hyperbolic singularities

Provided insights into accessory parameters on the Riemann sphere

Abstract

We propose the form of the Liouville action satisfying Polyakov conjecture on the accessory parameters for the hyperbolic singularities on the Riemann sphere.