Polyakov relation for the sphere and higher genus surfaces

Abstract

The Polyakov relation, which in the sphere topology gives the changes of the Liouville action under the variation of the position of the sources, in the case of higher genus is related also to the dependence of the action on the moduli of the surface. We write and prove such a relation for genus 1 and for all hyperelliptic surfaces.

31 pages;typos corrected;eq.(141) corrected

References in corpus (3)

• Classical Conformal Blocks and Painleve VI
• Classical torus conformal block, N=2* twisted superpotential and the accessory parameter of Lame equation
• Riemann-Hilbert treatment of Liouville theory on the torus

Cited by in corpus (6)

• Bootstrapping closed string field theory
• Hyperbolic string tadpole
• Torus classical conformal blocks
• Real analyticity of accessory parameters
• The continuation method and the real analyticity of the accessory parameters: the general elliptic case
• The continuation method and the real analyticity of the accessory parameters: the parabolic case