The continuation method and the real analyticity of the accessory parameters: the parabolic case

Abstract

We give the proof of the real analyticity of the accessory parameters in Liouville field theory as a function of the position of the sources in the case in which in addition to elliptic sources, parabolic sources are present. The method is a non trivial extension of the elliptic case as it requires in an intermediate step the introduction of a regulator. The treatment holds also in the case of the torus. A discussion is given of the extension to higher genus surfaces.

LaTeX, 39 pages, typos corrected

References in corpus (6)

• Virasoro vacuum block at next-to-leading order in the heavy-light limit
• Classical conformal blocks
• On the solution of Liouville equation
• Torus classical conformal blocks
• Real analyticity of accessory parameters
• The continuation method and the real analyticity of the accessory parameters: the general elliptic case