Remarks on irregular conformal blocks and Painlevé III and II tau functions

2018/04/13 by Nagoya, Hajime
#FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1804.04782

Abstract

We prove a conjecture on uniqueness and existence of the irregular vertex operators of rank r introduced in our previous paper. We also introduce ramified irregular vertex operators of the Virasoro algebra. As applications, we give conjectural formulas for series expansions of Painlevé III and II tau functions in terms of our ramified irregular conformal blocks.

Related

• Conformal blocks and Painlevé functions
• Many-faced Painlevé I: irregular conformal blocks, topological recursion, and holomorphic anomaly approaches
• Flat Connections from Irregular Conformal Blocks
• Higher conformal variations and the Virasoro vertex operator algebra
• Irregular conformal block and its matrix model