A note on rank 5/2 Liouville irregular block, Painlevé I and the H\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{H} $$\\end{document}0 Argyres-Douglas theory

Abstract

We study 4d type H\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{H} $$\\end{document}0 Argyres-Douglas theory in Ω-background by constructing Liouville irregular state of rank 5/2. The results are compared with generalized Holomorphic anomaly approach, which provides order by order expansion in Ω-background parameters ϵ1,2. Another crucial test of our results provides comparison with respect to Painlevé I τ-function, which was expected to be hold in self-dual case ϵ1 = −ϵ2. We also discuss Nekrasov-Shatashvili limit ϵ1 = 0, accessible either by means of deformed Seiberg-Witten curve, or WKB methods.